Господин Экзамен
Общий знаменатель 8*k+k^2+16*k^2/15+3*k/16-k^4/25-1
Решение
Вы ввели
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2 4
2 16*k 3*k k
8*k + k + ----- + --- - -- - 1
15 16 25
$$- \frac{k^{4}}{25} + k^{2} + \frac{16 k^{2}}{15} + \frac{3 k}{16} + 8 k - 1$$
8*k + k^2 + 16*k^2/15 + 3*k/16 - k^4/25 - 1*1
Разложение на множители
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/ _________________________________________________________________________________________________________________________________________________________________________________________________________________________\ / _________________________________________________________________________________________________________________________________________________________________________________________________________________________ \ / _________________________________________________________________________________________________________________________________________________________________________________________________________________________\ / _________________________________________________________________________________________________________________________________________________________________________________________________________________________\ | / _____________________________________ | | / _____________________________________ | | / _____________________________________ | | / _____________________________________ | | / / ________________ | | / / ________________ | | / / ________________ | | / / ________________ | | / 620 / 6555172625 125*\/ 29998275478665 26725 3275 | | / 620 / 6555172625 125*\/ 29998275478665 26725 3275 | | / 620 / 6555172625 125*\/ 29998275478665 26725 3275 | | / 620 / 6555172625 125*\/ 29998275478665 26725 3275 | | / --- - 2*3 / ---------- + ---------------------- - ---------------------------------------------- - ----------------------------------------------------------------------------------------------------------------- | | / --- - 2*3 / ---------- + ---------------------- - ---------------------------------------------- - ----------------------------------------------------------------------------------------------------------------- | | / --- - 2*3 / ---------- + ---------------------- - ---------------------------------------------- + ----------------------------------------------------------------------------------------------------------------- | | / --- - 2*3 / ---------- + ---------------------- - ---------------------------------------------- + ----------------------------------------------------------------------------------------------------------------- | | _____________________________________________________________________________________________________ / 9 \/ 2985984 331776 _____________________________________ _____________________________________________________________________________________________________ | | / 9 \/ 2985984 331776 _____________________________________ _____________________________________________________________________________________________________ _____________________________________________________________________________________________________| | _____________________________________________________________________________________________________ / 9 \/ 2985984 331776 _____________________________________ _____________________________________________________________________________________________________ | | _____________________________________________________________________________________________________ / 9 \/ 2985984 331776 _____________________________________ _____________________________________________________________________________________________________ | | / _____________________________________ / / ________________ / _____________________________________ | | / / ________________ / _____________________________________ / _____________________________________ | | / _____________________________________ / / ________________ / _____________________________________ | | / _____________________________________ / / ________________ / _____________________________________ | | / / ________________ / / 6555172625 125*\/ 29998275478665 / / ________________ | | / / 6555172625 125*\/ 29998275478665 / / ________________ / / ________________ | | / / ________________ / / 6555172625 125*\/ 29998275478665 / / ________________ | | / / ________________ / / 6555172625 125*\/ 29998275478665 / / ________________ | | / 310 / 6555172625 125*\/ 29998275478665 26725 / 162*3 / ---------- + ---------------------- / 310 / 6555172625 125*\/ 29998275478665 26725 | | / 162*3 / ---------- + ---------------------- / 310 / 6555172625 125*\/ 29998275478665 26725 / 310 / 6555172625 125*\/ 29998275478665 26725 | | / 310 / 6555172625 125*\/ 29998275478665 26725 / 162*3 / ---------- + ---------------------- / 310 / 6555172625 125*\/ 29998275478665 26725 | | / 310 / 6555172625 125*\/ 29998275478665 26725 / 162*3 / ---------- + ---------------------- / 310 / 6555172625 125*\/ 29998275478665 26725 | | / --- + 2*3 / ---------- + ---------------------- + ---------------------------------------------- / \/ 2985984 331776 8* / --- + 2*3 / ---------- + ---------------------- + ---------------------------------------------- | | / \/ 2985984 331776 8* / --- + 2*3 / ---------- + ---------------------- + ---------------------------------------------- / --- + 2*3 / ---------- + ---------------------- + ---------------------------------------------- | | / --- + 2*3 / ---------- + ---------------------- + ---------------------------------------------- / \/ 2985984 331776 8* / --- + 2*3 / ---------- + ---------------------- + ---------------------------------------------- | | / --- + 2*3 / ---------- + ---------------------- + ---------------------------------------------- / \/ 2985984 331776 8* / --- + 2*3 / ---------- + ---------------------- + ---------------------------------------------- | | / 9 \/ 2985984 331776 _____________________________________ / / 9 \/ 2985984 331776 _____________________________________ | | / / 9 \/ 2985984 331776 _____________________________________ / 9 \/ 2985984 331776 _____________________________________ | | / 9 \/ 2985984 331776 _____________________________________ / / 9 \/ 2985984 331776 _____________________________________ | | / 9 \/ 2985984 331776 _____________________________________ / / 9 \/ 2985984 331776 _____________________________________ | | / / ________________ / / / ________________ | | / / / ________________ / / ________________ | | / / ________________ / / / ________________ | | / / ________________ / / / ________________ | | / / 6555172625 125*\/ 29998275478665 / / / 6555172625 125*\/ 29998275478665 | | / / / 6555172625 125*\/ 29998275478665 / / 6555172625 125*\/ 29998275478665 | | / / 6555172625 125*\/ 29998275478665 / / / 6555172625 125*\/ 29998275478665 | | / / 6555172625 125*\/ 29998275478665 / / / 6555172625 125*\/ 29998275478665 | | / 162*3 / ---------- + ---------------------- / / 162*3 / ---------- + ---------------------- | | / / 162*3 / ---------- + ---------------------- / 162*3 / ---------- + ---------------------- | | / 162*3 / ---------- + ---------------------- / / 162*3 / ---------- + ---------------------- | | / 162*3 / ---------- + ---------------------- / / 162*3 / ---------- + ---------------------- | | \/ \/ 2985984 331776 \/ \/ \/ 2985984 331776 | | \/ \/ \/ 2985984 331776 \/ \/ 2985984 331776 | | \/ \/ 2985984 331776 \/ \/ \/ 2985984 331776 | | \/ \/ 2985984 331776 \/ \/ \/ 2985984 331776 | 1*|k + --------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|*|k + - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------|*|k + - --------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|*|k + - --------------------------------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| \ 2 2 / \ 2 2 / \ 2 2 / \ 2 2 /
$$\left(k + \left(\frac{\sqrt{\frac{26725}{162 \sqrt[3]{\frac{125 \sqrt{29998275478665}}{331776} + \frac{6555172625}{2985984}}} + 2 \sqrt[3]{\frac{125 \sqrt{29998275478665}}{331776} + \frac{6555172625}{2985984}} + \frac{310}{9}}}{2} - \frac{\sqrt{- \frac{3275}{8 \sqrt{\frac{26725}{162 \sqrt[3]{\frac{125 \sqrt{29998275478665}}{331776} + \frac{6555172625}{2985984}}} + 2 \sqrt[3]{\frac{125 \sqrt{29998275478665}}{331776} + \frac{6555172625}{2985984}} + \frac{310}{9}}} - 2 \sqrt[3]{\frac{125 \sqrt{29998275478665}}{331776} + \frac{6555172625}{2985984}} - \frac{26725}{162 \sqrt[3]{\frac{125 \sqrt{29998275478665}}{331776} + \frac{6555172625}{2985984}}} + \frac{620}{9}}}{2}\right)\right) 1 \left(k + \left(\frac{\sqrt{\frac{26725}{162 \sqrt[3]{\frac{125 \sqrt{29998275478665}}{331776} + \frac{6555172625}{2985984}}} + 2 \sqrt[3]{\frac{125 \sqrt{29998275478665}}{331776} + \frac{6555172625}{2985984}} + \frac{310}{9}}}{2} + \frac{\sqrt{- \frac{3275}{8 \sqrt{\frac{26725}{162 \sqrt[3]{\frac{125 \sqrt{29998275478665}}{331776} + \frac{6555172625}{2985984}}} + 2 \sqrt[3]{\frac{125 \sqrt{29998275478665}}{331776} + \frac{6555172625}{2985984}} + \frac{310}{9}}} - 2 \sqrt[3]{\frac{125 \sqrt{29998275478665}}{331776} + \frac{6555172625}{2985984}} - \frac{26725}{162 \sqrt[3]{\frac{125 \sqrt{29998275478665}}{331776} + \frac{6555172625}{2985984}}} + \frac{620}{9}}}{2}\right)\right) \left(k - \left(- \frac{\sqrt{- 2 \sqrt[3]{\frac{125 \sqrt{29998275478665}}{331776} + \frac{6555172625}{2985984}} - \frac{26725}{162 \sqrt[3]{\frac{125 \sqrt{29998275478665}}{331776} + \frac{6555172625}{2985984}}} + \frac{3275}{8 \sqrt{\frac{26725}{162 \sqrt[3]{\frac{125 \sqrt{29998275478665}}{331776} + \frac{6555172625}{2985984}}} + 2 \sqrt[3]{\frac{125 \sqrt{29998275478665}}{331776} + \frac{6555172625}{2985984}} + \frac{310}{9}}} + \frac{620}{9}}}{2} + \frac{\sqrt{\frac{26725}{162 \sqrt[3]{\frac{125 \sqrt{29998275478665}}{331776} + \frac{6555172625}{2985984}}} + 2 \sqrt[3]{\frac{125 \sqrt{29998275478665}}{331776} + \frac{6555172625}{2985984}} + \frac{310}{9}}}{2}\right)\right) \left(k - \left(\frac{\sqrt{- 2 \sqrt[3]{\frac{125 \sqrt{29998275478665}}{331776} + \frac{6555172625}{2985984}} - \frac{26725}{162 \sqrt[3]{\frac{125 \sqrt{29998275478665}}{331776} + \frac{6555172625}{2985984}}} + \frac{3275}{8 \sqrt{\frac{26725}{162 \sqrt[3]{\frac{125 \sqrt{29998275478665}}{331776} + \frac{6555172625}{2985984}}} + 2 \sqrt[3]{\frac{125 \sqrt{29998275478665}}{331776} + \frac{6555172625}{2985984}} + \frac{310}{9}}} + \frac{620}{9}}}{2} + \frac{\sqrt{\frac{26725}{162 \sqrt[3]{\frac{125 \sqrt{29998275478665}}{331776} + \frac{6555172625}{2985984}}} + 2 \sqrt[3]{\frac{125 \sqrt{29998275478665}}{331776} + \frac{6555172625}{2985984}} + \frac{310}{9}}}{2}\right)\right)$$
(((1*(k + (sqrt(310/9 + 2*(6555172625/2985984 + 125*sqrt(29998275478665)/331776)^(1/3) + 26725/(162*(6555172625/2985984 + 125*sqrt(29998275478665)/331776)^(1/3)))/2 + sqrt(620/9 - 2*(6555172625/2985984 + 125*sqrt(29998275478665)/331776)^(1/3) - 26725/(162*(6555172625/2985984 + 125*sqrt(29998275478665)/331776)^(1/3)) - 3275/(8*sqrt(310/9 + 2*(6555172625/2985984 + 125*sqrt(29998275478665)/331776)^(1/3) + 26725/(162*(6555172625/2985984 + 125*sqrt(29998275478665)/331776)^(1/3)))))/2)))*(k - (sqrt(620/9 - 2*(6555172625/2985984 + 125*sqrt(29998275478665)/331776)^(1/3) - 26725/(162*(6555172625/2985984 + 125*sqrt(29998275478665)/331776)^(1/3)) - 3275/(8*sqrt(310/9 + 2*(6555172625/2985984 + 125*sqrt(29998275478665)/331776)^(1/3) + 26725/(162*(6555172625/2985984 + 125*sqrt(29998275478665)/331776)^(1/3)))))/2 + sqrt(310/9 + 2*(6555172625/2985984 + 125*sqrt(29998275478665)/331776)^(1/3) + 26725/(162*(6555172625/2985984 + 125*sqrt(29998275478665)/331776)^(1/3)))/2)))*(k - (sqrt(310/9 + 2*(6555172625/2985984 + 125*sqrt(29998275478665)/331776)^(1/3) + 26725/(162*(6555172625/2985984 + 125*sqrt(29998275478665)/331776)^(1/3)))/2 + sqrt(620/9 - 2*(6555172625/2985984 + 125*sqrt(29998275478665)/331776)^(1/3) - 26725/(162*(6555172625/2985984 + 125*sqrt(29998275478665)/331776)^(1/3)) + 3275/(8*sqrt(310/9 + 2*(6555172625/2985984 + 125*sqrt(29998275478665)/331776)^(1/3) + 26725/(162*(6555172625/2985984 + 125*sqrt(29998275478665)/331776)^(1/3)))))/2)))*(k - (sqrt(310/9 + 2*(6555172625/2985984 + 125*sqrt(29998275478665)/331776)^(1/3) + 26725/(162*(6555172625/2985984 + 125*sqrt(29998275478665)/331776)^(1/3)))/2 - sqrt(620/9 - 2*(6555172625/2985984 + 125*sqrt(29998275478665)/331776)^(1/3) - 26725/(162*(6555172625/2985984 + 125*sqrt(29998275478665)/331776)^(1/3)) + 3275/(8*sqrt(310/9 + 2*(6555172625/2985984 + 125*sqrt(29998275478665)/331776)^(1/3) + 26725/(162*(6555172625/2985984 + 125*sqrt(29998275478665)/331776)^(1/3)))))/2))
Общее упрощение
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4 2
k 31*k 131*k
-1 - -- + ----- + -----
25 15 16
$$- \frac{k^{4}}{25} + \frac{31 k^{2}}{15} + \frac{131 k}{16} - 1$$
-1 - k^4/25 + 31*k^2/15 + 131*k/16
Разложение дроби
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-1 - k^4/25 + 31*k^2/15 + 131*k/16
$$- \frac{k^{4}}{25} + \frac{31 k^{2}}{15} + \frac{131 k}{16} - 1$$
4 2
k 31*k 131*k
-1 - -- + ----- + -----
25 15 16
Собрать выражение
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4 2
k 31*k 131*k
-1 - -- + ----- + -----
25 15 16
$$- \frac{k^{4}}{25} + \frac{31 k^{2}}{15} + \frac{131 k}{16} - 1$$
-1 - k^4/25 + 31*k^2/15 + 131*k/16
Комбинаторика
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4 2
k 31*k 131*k
-1 - -- + ----- + -----
25 15 16
$$- \frac{k^{4}}{25} + \frac{31 k^{2}}{15} + \frac{131 k}{16} - 1$$
-1 - k^4/25 + 31*k^2/15 + 131*k/16
Численный ответ
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-1.0 + 8.1875*k + 2.06666666666667*k^2 - 0.04*k^4
-1.0 + 8.1875*k + 2.06666666666667*k^2 - 0.04*k^4
Степени
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4 2
k 31*k 131*k
-1 - -- + ----- + -----
25 15 16
$$- \frac{k^{4}}{25} + \frac{31 k^{2}}{15} + \frac{131 k}{16} - 1$$
-1 - k^4/25 + 31*k^2/15 + 131*k/16
Рациональный знаменатель
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4 2
-6000 - 240*k + 12400*k + 49125*k
-----------------------------------
6000
$$\frac{- 240 k^{4} + 12400 k^{2} + 49125 k - 6000}{6000}$$
4 2
k 31*k 131*k
-1 - -- + ----- + -----
25 15 16
$$- \frac{k^{4}}{25} + \frac{31 k^{2}}{15} + \frac{131 k}{16} - 1$$
-1 - k^4/25 + 31*k^2/15 + 131*k/16
Объединение рациональных выражений
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4 2
-1200 - 48*k + 2480*k + 9825*k
--------------------------------
1200
$$\frac{- 48 k^{4} + 2480 k^{2} + 9825 k - 1200}{1200}$$
(-1200 - 48*k^4 + 2480*k^2 + 9825*k)/1200
Общий знаменатель
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4 2
k 31*k 131*k
-1 - -- + ----- + -----
25 15 16
$$- \frac{k^{4}}{25} + \frac{31 k^{2}}{15} + \frac{131 k}{16} - 1$$
-1 - k^4/25 + 31*k^2/15 + 131*k/16