How do you simplify #2/(x-1) + (x-11)/(x^2+3x-4)#?

1 Answer
Mar 18, 2016

#3/(x+4)#

Explanation:

#1#. Factor the denominator of the second fraction.

#2/(x-1)+(x-11)/(x^2+3x-4)#

#=2/(x-1)+(x-11)/((x+4)(x-1))#

#2#. To add the two fractions together, find its L.C.D. (lowest common denominator).

#=(2color(blue)((x+4)))/((x-1)color(blue)((x+4)))+(x-11)/((x+4)(x-1))#

#=(2color(blue)((x+4))+(x-11))/((x+4)(x-1))#

#3#. Simplify the numerator.

#=(2x+8+x-11)/((x+4)(x-1))#

#=(3x-3)/((x+4)(x-1))#

#4#. Factor out #3# from the numerator.

#=(3(x-1))/((x+4)(x-1))#

#5#. Since the factor, #(x-1)#, appears in both the numerator and denominator, they cancel out.

#=(3color(red)cancelcolor(black)((x-1)))/((x+4)color(red)cancelcolor(black)((x-1)))#

#=color(green)(|bar(ul(color(white)(a/a)3/(x+4)color(white)(a/a)|)))#