Question

Find the difference of the question below I have the question and answer choices listed. Any incorrect answers or links will be removed.Thanks in advance <3

Answer 1

Given :

`(5x)/(x^2-x-6)-(4)/(x^2+4x+4)`

We need to factor the polynomial in the denominator.

`(5x)/(x^2-x-6)-(4)/(x^2+4x+4)=(5x)/(x^2-3x+2x-6)-(4)/(x^2+2*2x+2^2)`

`=\frac{5x}{x(x^{}-3)+2(x-3)}-(4)/((x+2)^2)`

`=\frac{5x}{(x^{}-3)(x+2)}-(4)/((x+2)^2)`

The least common multiple of (x-3)(x+2) and (x+2)(x+2) is (x-3)(x+2)(x+2), so making the denominatore (x-3)(x+2)(x+2).

`=\frac{5x(x+2)}{(x^{}-3)(x+2)^2}-(4(x-3))/((x-3)(x+2)^2)`

`=\frac{5x^2+10x}{(x^{}-3)(x+2)^2}-(4x-12)/((x-3)(x+2)^2)`

`=\frac{5x^2+10x-4x+12}{(x^{}-3)(x+2)^2}`

`=\frac{5x^2+6x+12}{(x^{}-3)(x+2)^2}`

Hence the difference of the given is

`\frac{5x^2+6x+12}{(x^{}-3)(x+2)^2}`