Question

#82 will give brainliest to best answer!​

Answer 1

Answer:

$\frac{6}{k-6}$

Step-by-step explanation:

First, we can factor all of the following equations to turn that weird, huge looking thing into $\frac{(k+6)(k-6)}{(k-6)(k-10)}$ ÷ $\frac{(k-6)^2}{k(k-6)}$ × $\frac{6(k-10)}{k(k + 6)}$. We know that division is simply multiplication by the reciprocal, so that whole equation will turn into $\frac{(k+6)(k-6)}{(k-6)(k-10)}$ × $\frac{k(k-6)}{(k-6)^2}$ × $\frac{6(k-10)}{k(k+6)}$. Now we can cancel out some values if they are both in the numerator and denominator, which will turn that still huge looking thing into $\frac{6}{k-6}$ which is our final answer, as it cannot be simplified further.

Hope this helped! :)

Answer 2

(K^2-36/k^2-16k+60)/(k^2-12k+36/k^2-6k)*(6k-60/k^2+6k)

=[(k^2-6^2)/(k-6)(k-10)]*[k(k-6)/(k-6)^2][6(k-10)/k(k+6)

=(k^2-6^2)(k/(k-6)^2)(6/k (k-6)
=6(k^2-6^2)/(k-6)^2(k+6)