Question

Subtract (In picture)

Answer 1

--First we have to simplfy

$\frac{2x-8}{x^2-x-12} -\frac{x-3}{x(x+1)}$

$\frac{2(x-4)}{(x-4)(x+3)} - \frac{x-3}{x(x+1)}$

--Cancel common factors

$\frac{2}{(x+3)} -\frac{x-3}{x(x+1)}$

--Here remember never cancel factors in a subtraction or addition problem

--Now Multiply each side until both denominators are equal to each other

$\frac{2[x(x+1)]}{x(x+3)(x+1)} -\frac{(x-3)(x+3)}{x(x+3)(x+1)}$

--Simplify

$\frac{2x^2+2x}{x(x+1)(x+3)} - \frac{x^2-9}{x(x+1)(x+3)}$

--Now that the denominators are the same: subtract!

$\frac{2x^2+2x-(x^2-9)}{x(x+1)(x+3)}$

$\frac{2x^2-x^2+2x+9}{x(x+1)(x+3)}$

--And LAST STEP! ......Simplify More.... To get your answer

$\frac{x^2+2x+9}{x(x+1)(x+3)}$