Question

How do you simplify `4/(x-2)-3/(x+1)+2/(x^2-x-2)`?

Answer 1

`(x+12)/((x-2)(x+1))=(x+12)/(x^2-x-2)`

Explanation:

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

We need the denominators to be the same. We can do that by multiplying through with various forms of the number 1:

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

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

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

`(4x+4)/((x-2)(x+1))-(3x-6)/((x+1)(x-2))+2/((x-2)(x+1))`

`((4x+4)-(3x-6)+2)/((x-2)(x+1))`

`(4x+4-3x+6+2)/((x-2)(x+1))`

`(x+12)/((x-2)(x+1))=(x+12)/(x^2-x-2)`