Question

The following equation is true for all real values of k for which the expression on the left is defined, and A

is a polynomial expression.
6k2 – 36k k2 + 12k + 36
А
k2 - 36
1
What is A?

Answer 1

A = 6k(k + 6)

Explanation:

We have to solve the given equation for the value of A,

`(6k^2-36k)/(A).(k^2+12k+36)/(k^2-36)=1`

`((6k^2-36k)(k^2+12k+36))/(A(k^2-36))=1`

(6k² - 36k)(k² + 12k + 36) = A(k² -36)

6k(k - 6)(k + 6)² = A(k - 6)(k + 6)

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

A = 6k(k + 6)

Therefore, value of A is 6k(k + 6).