# How do you simplify #x/(x-3)-3/(x+2)#?

##### 1 Answer

Apr 8, 2017

#### Explanation:

Before we can subtract fractions we require them to have a

#color(blue)"common denominator"# To obtain a common denominator for both fractions.

#•"multiply numerator/denominator of " 3/(x+2)"by " (x-3)#

#rArr(xcolor(red)((x+2)))/((x-3)color(red)((x+2)))-(3color(red)((x-3)))/(color(red)((x-3))(x+2))# Now there is a common denominator, subtract the numerators leaving the denominator as it is.

#=(x(x+2)-3(x-3))/((x-3)(x+2))# distribute the numerator and simplify.

#=(x^2+2x-3x+9)/((x-3)(x+2))#

#=(x^2-x+9)/((x-3)(x+2))#