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

1 Answer
Jan 14, 2017

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)#