Question

How do you simplify `x/(x+3) - (x+3)/x`?

Answer 1

See the entire simplification process below:

Explanation:

In order to subtract to fractions they need to be over a common denominator. In this case `x(x +3)`, Therefore, we need to multiply each fraction by the appropriate form of `1`:

`(x/x xx x/(x + 3)) - ((x + 3)/(x + 3) xx (x + 3)/x) ->`

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

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

`(x^2 - x^2 - 6x - 9)/(x(x + 3))`

`(0 - 6x - 9)/(x(x + 3))`

`(-6x - 9)/(x(x + 3))`

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

or

`(-6x - 9)/(x^2 + 3x)`