Question

Subtract (In picture)

Answer 1

--First we have to simplfy

`(2x-8)/(x^2-x-12) -(x-3)/(x(x+1))`

`(2(x-4))/((x-4)(x+3)) - (x-3)/(x(x+1))`

--Cancel common factors

`(2)/((x+3)) -(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

`(2[x(x+1)])/(x(x+3)(x+1)) -((x-3)(x+3))/(x(x+3)(x+1))`

--Simplify

`(2x^2+2x)/(x(x+1)(x+3)) - (x^2-9)/(x(x+1)(x+3))`

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

`(2x^2+2x-(x^2-9))/(x(x+1)(x+3))`

`(2x^2-x^2+2x+9)/(x(x+1)(x+3))`

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

`(x^2+2x+9)/(x(x+1)(x+3))`