Рациональный знаменатель
[src]
/ 2\
\-81 + t /*((1 + 54*t)*(9 + t) + (-1 + 54*t)*(-9 + t))
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/ 2\
\1 + 6*t /*(-9 + t)*(9 + t)
$$\frac{\left(t^{2} - 81\right) \left(\left(t - 9\right) \left(54 t - 1\right) + \left(t + 9\right) \left(54 t + 1\right)\right)}{\left(t - 9\right) \left(t + 9\right) \left(6 t^{2} + 1\right)}$$
2 2 3 3
81 81 t t 4374*t 4374*t 54*t 54*t
- --------------------- + -------------------- + --------------------- - -------------------- - --------------------- - -------------------- + --------------------- + --------------------
2 3 3 2 2 3 3 2 2 3 3 2 2 3 3 2
-9 + t - 54*t + 6*t 9 + t + 6*t + 54*t -9 + t - 54*t + 6*t 9 + t + 6*t + 54*t -9 + t - 54*t + 6*t 9 + t + 6*t + 54*t -9 + t - 54*t + 6*t 9 + t + 6*t + 54*t
$$\frac{54 t^{3}}{6 t^{3} + 54 t^{2} + t + 9} + \frac{54 t^{3}}{6 t^{3} - 54 t^{2} + t - 9} - \frac{t^{2}}{6 t^{3} + 54 t^{2} + t + 9} + \frac{t^{2}}{6 t^{3} - 54 t^{2} + t - 9} - \frac{4374 t}{6 t^{3} + 54 t^{2} + t + 9} - \frac{4374 t}{6 t^{3} - 54 t^{2} + t - 9} + \frac{81}{6 t^{3} + 54 t^{2} + t + 9} - \frac{81}{6 t^{3} - 54 t^{2} + t - 9}$$
-81/(-9 + t - 54*t^2 + 6*t^3) + 81/(9 + t + 6*t^3 + 54*t^2) + t^2/(-9 + t - 54*t^2 + 6*t^3) - t^2/(9 + t + 6*t^3 + 54*t^2) - 4374*t/(-9 + t - 54*t^2 + 6*t^3) - 4374*t/(9 + t + 6*t^3 + 54*t^2) + 54*t^3/(-9 + t - 54*t^2 + 6*t^3) + 54*t^3/(9 + t + 6*t^3 + 54*t^2)
Объединение рациональных выражений
[src]
/ 2\
\-81 + t /*((1 + 54*t)*(9 + t) + (-1 + 54*t)*(-9 + t))
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/ 2\
\1 + 6*t /*(-9 + t)*(9 + t)
$$\frac{\left(t^{2} - 81\right) \left(\left(t - 9\right) \left(54 t - 1\right) + \left(t + 9\right) \left(54 t + 1\right)\right)}{\left(t - 9\right) \left(t + 9\right) \left(6 t^{2} + 1\right)}$$
(-81 + t^2)*((1 + 54*t)*(9 + t) + (-1 + 54*t)*(-9 + t))/((1 + 6*t^2)*(-9 + t)*(9 + t))
/ 2\ /1 + 54*t -1 + 54*t\
\-81 + t /*|-------- + ---------|
\ -9 + t 9 + t /
---------------------------------
2
1 + 6*t
$$\frac{\left(t^{2} - 81\right) \left(\frac{54 t - 1}{t + 9} + \frac{54 t + 1}{t - 9}\right)}{6 t^{2} + 1}$$
(-81 + t^2)*((1 + 54*t)/(-9 + t) + (-1 + 54*t)/(9 + t))/(1 + 6*t^2)
/ 2\ /1 + 54*t -1 + 54*t\
\-81 + t /*|-------- + ---------|
\ -9 + t 9 + t /
---------------------------------
2
1 + 6*t
$$\frac{\left(t^{2} - 81\right) \left(\frac{54 t - 1}{t + 9} + \frac{54 t + 1}{t - 9}\right)}{6 t^{2} + 1}$$
(-81 + t^2)*((1 + 54*t)/(-9 + t) + (-1 + 54*t)/(9 + t))/(1 + 6*t^2)