How do you simplify #x/(x+2) - x/(x-2) #?

1 Answer
Oct 8, 2015

Answer:

#-(4x)/((x-2)(x+2))#

Explanation:

You need to find the common denominator of the two fractions. Notice that you can multiply the first fraction by #1 = (x-2)/(x-2)# and the second fraction by #1 = (x+2)/(x+2)# to get

#x/(x+2) * (x-2)/(x-2) - x/(x-2) * (x+2)/(x+2)#

#( x * (x-2))/((x-2)(x+2)) - ( x * (x+2))/((x-2)(x+2))#

Expand the parantheses in the numerator to cancel out like terms

#( color(red)(cancel(color(black)(x^2))) - 2x - color(red)(cancel(color(black)(x^2))) - 2x)/((x-2)(x+2))#

The final form of the expression will thus be

#-(4x)/((x-2)(x+2))#