Question

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

Answer 1

`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)|)))`