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

1 Answer
Sep 14, 2016

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))