Factor completely and write the answer with no negative exponents. Do not rationalize the denominator.

$\dfrac{6(t-1)^5(2t+5)^6-6(2t+5)^5(2)(t-1)^6}{[(2t+5)^6]^2}$

Solution

VerifiedCancelling the common factor between the numerator and the denominator, the given expression, $\dfrac{6(t-1)^5(2t+5)^6-6(2t+5)^5(2)(t-1)^6}{[(2t+5)^6]^2} ,$ simplifies to

$\begin{align*} & \dfrac{6(t-1)^5(2t+5)^6-6(2t+5)^5(2)(t-1)^6}{(2t+5)^{6(2)}} &\left( \text{use }(a^m)^n=a^{mn} \right) \\\\&= \dfrac{6(t-1)^5(2t+5)^6-6(2t+5)^5(2)(t-1)^6}{(2t+5)^{12}} \\\\&= \dfrac{(2t+5)^5\left[ 6(t-1)^5(2t+5)-6(2)(t-1)^6 \right]}{(2t+5)^{12}} &\left( \text{factor }(2t+5)^5 \right) \\\\&= \dfrac{\cancel{(2t+5)^5}\left[ 6(t-1)^5(2t+5)-6(2)(t-1)^6 \right]}{(2t+5)^{\cancel{12}7}} &\left( \text{factor }(2t+5)^5 \right) \\\\&= \dfrac{ 6(t-1)^5(2t+5)-6(2)(t-1)^6 }{(2t+5)^{7}} \\\\&= \dfrac{ 1 }{(2t+5)^{7}}\cdot6(t-1)^5(2t+5)-6(2)(t-1)^6 .\end{align*}$

## Create an account to view solutions

## Create an account to view solutions

## Recommended textbook solutions

#### College Algebra and Trigonometry

1st Edition•ISBN: 9780078035623Donna Gerken, Julie Miller#### Algebra and Trigonometry

4th Edition•ISBN: 9781305071742 (2 more)Lothar Redlin, Stewart, Watson## More related questions

1/4

1/7