Answer:
A = 6k(k + 6)
Step-by-step explanation:
We have to solve the given equation for the value of A,
[tex]\frac{6k^2-36k}{A}.\frac{k^2+12k+36}{k^2-36}=1[/tex]
[tex]\frac{(6k^2-36k)(k^2+12k+36)}{A(k^2-36)}=1[/tex]
(6k² - 36k)(k² + 12k + 36) = A(k² -36)
6k(k - 6)(k + 6)² = A(k - 6)(k + 6)
A = [tex]\frac{6k(k-6)(k+6)^2}{(k-6)(k+6)}[/tex]
A = 6k(k + 6)
Therefore, value of A is 6k(k + 6).
