Question

How do you subtract `9/(x-2)-5/(x+4)`?

Answer 1

`9/(x-2)-5/(x+4) = (2(x+23))/((x-2)(x+4))`

Explanation:

To subtract fractions you need a common denominator, so let's use `(x-2)(x+4)` as our common denominator:

`9/(x-2)-5/(x+4) = (9(x+4))/((x-2)(x+4))-(5(x-2))/((x-2)(x+4))`

`color(white)(9/(x-2)-5/(x+4)) = (9(x+4)-5(x-2))/((x-2)(x+4))`

`color(white)(9/(x-2)-5/(x+4)) = (9x+36-5x+10)/((x-2)(x+4))`

`color(white)(9/(x-2)-5/(x+4)) = (4x+46)/((x-2)(x+4))`

`color(white)(9/(x-2)-5/(x+4)) = (2(x+23))/((x-2)(x+4))`