Господин Экзамен
Упрощение выражений/
Общий знаменатель/
(a-c)*(a^3-c^3)*(1+c/(a-c)-(1+c)/c)*c/((a^2+a*c+c^2)*(a^2*b-b*c^2)*(c*(1+c)-a)*b)
Общий знаменатель (a-c)*(a^3-c^3)*(1+c/(a-c)-(1+c)/c)*c/((a^2+a*c+c^2)*(a^2*b-b*c^2)*(c*(1+c)-a)*b)
Решение
Вы ввели
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/ 3 3\ / c 1 + c\
(a - c)*\a - c /*|1 + ----- - -----|*c
\ a - c c /
-----------------------------------------------
/ 2 2\ / 2 2\
\a + a*c + c /*\a *b - b*c /*(c*(1 + c) - a)*b
$$\frac{c \left(a - c\right) \left(a^{3} - c^{3}\right) \left(\frac{c}{a - c} + 1 - \frac{c + 1}{c}\right)}{b \left(c \left(c + 1\right) - a\right) \left(a^{2} b - b c^{2}\right) \left(a^{2} + a c + c^{2}\right)}$$
(a - c)*(a^3 - c^3)*(1 + c/(a - c) - (1 + c)/c)*c/(((a^2 + a*c + c^2)*(a^2*b - b*c^2)*(c*(1 + c) - a)*b))
Общее упрощение
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1 ---------- 2 b *(a + c)
$$\frac{1}{b^{2} \left(a + c\right)}$$
1/(b^2*(a + c))
Численный ответ
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c*(a - c)*(a^3 - c^3)*(1.0 + c/(a - c) - (1.0 + c)/c)/(b*(-a + c*(1.0 + c))*(b*a^2 - b*c^2)*(a^2 + c^2 + a*c))
c*(a - c)*(a^3 - c^3)*(1.0 + c/(a - c) - (1.0 + c)/c)/(b*(-a + c*(1.0 + c))*(b*a^2 - b*c^2)*(a^2 + c^2 + a*c))
Комбинаторика
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1 ---------- 2 b *(a + c)
$$\frac{1}{b^{2} \left(a + c\right)}$$
1/(b^2*(a + c))
Собрать выражение
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/ 3 3\ / c 1 + c\
c*(a - c)*\a - c /*|1 + ----- - -----|
\ a - c c /
---------------------------------------------
2 / 2 2\ / 2 2 \
b *\a - c /*(-a + c*(1 + c))*\a + c + a*c/
$$\frac{c \left(a - c\right) \left(a^{3} - c^{3}\right) \left(\frac{c}{a - c} + 1 - \frac{c + 1}{c}\right)}{b^{2} \left(c \left(c + 1\right) - a\right) \left(a^{2} - c^{2}\right) \left(a^{2} + a c + c^{2}\right)}$$
/ 3 3\ / c -1 - c\
c*(a - c)*\a - c /*|1 + ----- + ------|
\ a - c c /
------------------------------------------------
/ 2 2\ / 2 2 \
b*(-a + c*(1 + c))*\b*a - b*c /*\a + c + a*c/
$$\frac{c \left(a - c\right) \left(a^{3} - c^{3}\right) \left(\frac{c}{a - c} + 1 + \frac{- c - 1}{c}\right)}{b \left(c \left(c + 1\right) - a\right) \left(a^{2} b - b c^{2}\right) \left(a^{2} + a c + c^{2}\right)}$$
c*(a - c)*(a^3 - c^3)*(1 + c/(a - c) + (-1 - c)/c)/(b*(-a + c*(1 + c))*(b*a^2 - b*c^2)*(a^2 + c^2 + a*c))
Общий знаменатель
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1 ----------- 2 2 a*b + c*b
$$\frac{1}{a b^{2} + b^{2} c}$$
1/(a*b^2 + c*b^2)
Рациональный знаменатель
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4 4 5 3 3 3 2
- a - c - c + a*c + c*a + a *c
--------------------------------------------
/ 2 2\ / 2 \ / 2 2 \
b*\b*a - b*c /*\c + c - a/*\a + c + a*c/
$$\frac{a^{3} c^{2} - c^{5} - a^{4} + a^{3} c + a c^{3} - c^{4}}{b \left(a^{2} b - b c^{2}\right) \left(c^{2} - a + c\right) \left(a^{2} + a c + c^{2}\right)}$$
6 4 4 3 3 4 2 5 3 3
c a c a*c c*a a *c a*c a *c
------------------------------------------------------------------------------------------------ - ----------------------------------------------------------------------------- - ----------------------------------------------------------------------------- + ----------------------------------------------------------------------------- + ----------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------ - ------------------------------------------------------------------------------------------------ - ------------------------------------------------------------------------------------------------
2 6 2 7 6 2 5 2 4 2 2 5 2 2 2 5 2 2 4 2 2 5 3 2 4 5 2 2 5 2 6 2 2 3 3 2 2 3 2 3 4 2 2 2 5 5 2 2 5 2 6 2 2 3 3 2 2 3 2 3 4 2 2 2 5 5 2 2 5 2 6 2 2 3 3 2 2 3 2 3 4 2 2 2 5 5 2 2 5 2 6 2 2 3 3 2 2 3 2 3 4 2 2 2 5 2 6 2 7 6 2 5 2 4 2 2 5 2 2 2 5 2 2 4 2 2 5 3 2 4 2 6 2 7 6 2 5 2 4 2 2 5 2 2 2 5 2 2 4 2 2 5 3 2 4 2 6 2 7 6 2 5 2 4 2 2 5 2 2 2 5 2 2 4 2 2 5 3 2 4
b *c + b *c - a *b + c*a *b + a *b *c + a *b *c - a*b *c - a *b *c - a *b *c - a *b *c - a *b - b *c - b *c + a *b *c + a *b *c + a *b *c + a *b *c - a*b *c - a *b - b *c - b *c + a *b *c + a *b *c + a *b *c + a *b *c - a*b *c - a *b - b *c - b *c + a *b *c + a *b *c + a *b *c + a *b *c - a*b *c - a *b - b *c - b *c + a *b *c + a *b *c + a *b *c + a *b *c - a*b *c b *c + b *c - a *b + c*a *b + a *b *c + a *b *c - a*b *c - a *b *c - a *b *c - a *b *c b *c + b *c - a *b + c*a *b + a *b *c + a *b *c - a*b *c - a *b *c - a *b *c - a *b *c b *c + b *c - a *b + c*a *b + a *b *c + a *b *c - a*b *c - a *b *c - a *b *c - a *b *c
$$\frac{a^{4} c^{2}}{a^{5} b^{2} c^{2} - a^{3} b^{2} c^{4} - a^{2} b^{2} c^{5} + b^{2} c^{7} - a^{6} b^{2} + a^{5} b^{2} c + a^{4} b^{2} c^{2} - a^{2} b^{2} c^{4} - a b^{2} c^{5} + b^{2} c^{6}} - \frac{a^{3} c^{3}}{a^{5} b^{2} c^{2} - a^{3} b^{2} c^{4} - a^{2} b^{2} c^{5} + b^{2} c^{7} - a^{6} b^{2} + a^{5} b^{2} c + a^{4} b^{2} c^{2} - a^{2} b^{2} c^{4} - a b^{2} c^{5} + b^{2} c^{6}} - \frac{a c^{5}}{a^{5} b^{2} c^{2} - a^{3} b^{2} c^{4} - a^{2} b^{2} c^{5} + b^{2} c^{7} - a^{6} b^{2} + a^{5} b^{2} c + a^{4} b^{2} c^{2} - a^{2} b^{2} c^{4} - a b^{2} c^{5} + b^{2} c^{6}} + \frac{c^{6}}{a^{5} b^{2} c^{2} - a^{3} b^{2} c^{4} - a^{2} b^{2} c^{5} + b^{2} c^{7} - a^{6} b^{2} + a^{5} b^{2} c + a^{4} b^{2} c^{2} - a^{2} b^{2} c^{4} - a b^{2} c^{5} + b^{2} c^{6}} - \frac{a^{4}}{a^{4} b^{2} c^{2} + a^{3} b^{2} c^{3} - a b^{2} c^{5} - b^{2} c^{6} - a^{5} b^{2} + a^{3} b^{2} c^{2} + a^{2} b^{2} c^{3} - b^{2} c^{5}} + \frac{a^{3} c}{a^{4} b^{2} c^{2} + a^{3} b^{2} c^{3} - a b^{2} c^{5} - b^{2} c^{6} - a^{5} b^{2} + a^{3} b^{2} c^{2} + a^{2} b^{2} c^{3} - b^{2} c^{5}} + \frac{a c^{3}}{a^{4} b^{2} c^{2} + a^{3} b^{2} c^{3} - a b^{2} c^{5} - b^{2} c^{6} - a^{5} b^{2} + a^{3} b^{2} c^{2} + a^{2} b^{2} c^{3} - b^{2} c^{5}} - \frac{c^{4}}{a^{4} b^{2} c^{2} + a^{3} b^{2} c^{3} - a b^{2} c^{5} - b^{2} c^{6} - a^{5} b^{2} + a^{3} b^{2} c^{2} + a^{2} b^{2} c^{3} - b^{2} c^{5}}$$
c^6/(b^2*c^6 + b^2*c^7 - a^6*b^2 + c*a^5*b^2 + a^4*b^2*c^2 + a^5*b^2*c^2 - a*b^2*c^5 - a^2*b^2*c^4 - a^2*b^2*c^5 - a^3*b^2*c^4) - a^4/(-a^5*b^2 - b^2*c^5 - b^2*c^6 + a^2*b^2*c^3 + a^3*b^2*c^2 + a^3*b^2*c^3 + a^4*b^2*c^2 - a*b^2*c^5) - c^4/(-a^5*b^2 - b^2*c^5 - b^2*c^6 + a^2*b^2*c^3 + a^3*b^2*c^2 + a^3*b^2*c^3 + a^4*b^2*c^2 - a*b^2*c^5) + a*c^3/(-a^5*b^2 - b^2*c^5 - b^2*c^6 + a^2*b^2*c^3 + a^3*b^2*c^2 + a^3*b^2*c^3 + a^4*b^2*c^2 - a*b^2*c^5) + c*a^3/(-a^5*b^2 - b^2*c^5 - b^2*c^6 + a^2*b^2*c^3 + a^3*b^2*c^2 + a^3*b^2*c^3 + a^4*b^2*c^2 - a*b^2*c^5) + a^4*c^2/(b^2*c^6 + b^2*c^7 - a^6*b^2 + c*a^5*b^2 + a^4*b^2*c^2 + a^5*b^2*c^2 - a*b^2*c^5 - a^2*b^2*c^4 - a^2*b^2*c^5 - a^3*b^2*c^4) - a*c^5/(b^2*c^6 + b^2*c^7 - a^6*b^2 + c*a^5*b^2 + a^4*b^2*c^2 + a^5*b^2*c^2 - a*b^2*c^5 - a^2*b^2*c^4 - a^2*b^2*c^5 - a^3*b^2*c^4) - a^3*c^3/(b^2*c^6 + b^2*c^7 - a^6*b^2 + c*a^5*b^2 + a^4*b^2*c^2 + a^5*b^2*c^2 - a*b^2*c^5 - a^2*b^2*c^4 - a^2*b^2*c^5 - a^3*b^2*c^4)
Объединение рациональных выражений
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/ 3 3\ / 2 \ \a - c /*\c + c*(a - c) - (1 + c)*(a - c)/ --------------------------------------------- 2 / 2 2\ / 2 2 \ b *\a - c /*(-a + c*(1 + c))*\a + c + a*c/
$$\frac{\left(a^{3} - c^{3}\right) \left(c^{2} + c \left(a - c\right) - \left(a - c\right) \left(c + 1\right)\right)}{b^{2} \left(c \left(c + 1\right) - a\right) \left(a^{2} - c^{2}\right) \left(a^{2} + a c + c^{2}\right)}$$
(a^3 - c^3)*(c^2 + c*(a - c) - (1 + c)*(a - c))/(b^2*(a^2 - c^2)*(-a + c*(1 + c))*(a^2 + c^2 + a*c))
Степени
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/ 3 3\ / c -1 - c\
c*(a - c)*\a - c /*|1 + ----- + ------|
\ a - c c /
------------------------------------------------
/ 2 2\ / 2 2 \
b*(-a + c*(1 + c))*\b*a - b*c /*\a + c + a*c/
$$\frac{c \left(a - c\right) \left(a^{3} - c^{3}\right) \left(\frac{c}{a - c} + 1 + \frac{- c - 1}{c}\right)}{b \left(c \left(c + 1\right) - a\right) \left(a^{2} b - b c^{2}\right) \left(a^{2} + a c + c^{2}\right)}$$
/ 3 3\ / c -1 - c\
c*(a - c)*\a - c /*|1 + ----- + ------|
\ a - c c /
-----------------------------------------------
/ 2 2\ / 2 2\
b*(c*(1 + c) - a)*\a *b - b*c /*\a + a*c + c /
$$\frac{c \left(a - c\right) \left(a^{3} - c^{3}\right) \left(\frac{c}{a - c} + 1 + \frac{- c - 1}{c}\right)}{b \left(c \left(c + 1\right) - a\right) \left(a^{2} b - b c^{2}\right) \left(a^{2} + a c + c^{2}\right)}$$
c*(a - c)*(a^3 - c^3)*(1 + c/(a - c) + (-1 - c)/c)/(b*(c*(1 + c) - a)*(a^2*b - b*c^2)*(a^2 + a*c + c^2))