Question

Find the difference 5x/x^2-x-6 (-) 4/x^2+4x+4

Answer 1

Answer:

$\frac{5x^2+6x+12}{x^3+x^2-8x-12}$

Step-by-step explanation:

We want to find the difference;

$\frac{5x}{x^2-x-6} -\frac{4}{x^2+4x+4}$

We factor the denominators to get;

$\frac{5x}{(x+2)(x-3)} -\frac{4}{(x+2)^2}$

The LCD is $(x+2)^2(x-3)$

$\frac{5x(x+2)-4(x-3)}{(x+2)^2(x-3)}$

Expand

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

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

$\frac{5x^2+6x+12}{x^3+x^2-8x-12}$