Question

How do you simplify `x/(x+5)+(5x)/(x-5)`?

Answer 1

Convert the terms to a common denominator then add the numerators and simplify.

`color(white)("XXX")(2x(3x-10))/(x^2-25)`

Explanation:

`x/(x+5)+(5x)/(x-5)`

`color(white)("XXX")= (x(x-5))/((x+5)(x-5)) + (5x(x+5))/((x+5)(x-5))`

`color(white)("XXX")=(x^2-5x+5x^2+25x)/((x+5)(x-5))`

`color(white)("XXX")=(6x^2-20x)/((x+5)(x-5))`

`color(white)("XXX")=(2x(3x-10))/(x^2-25)`