Simplify the rational expression. State any restrictions on the variable? Please check my answer/correct it

6/((x^2-16)-2/((x^2-x-12)

My Answer: 4/((x+4)(x+3)
restrictions: x=-4,4,-3

1 Answer
Apr 13, 2018

Restrictions look good, might have been oversimplified.

Explanation:

(6/(x^2-16))-(2/(x^2-x-12))
Factoring bottom parts:
=(6/((x+4)(x-4)))-(2/((x-4)(x+3)))
Multiply left by ((x+3)/(x+3)) and right by ((x+4)/(x+4)) (common denomanators)
=(6(x+3))/((x+4)(x-4)(x+3)) - (2(x+4))/((x-4)(x+3)(x+4))
Which simplifies to:
((4x+10)/((x+4)(x-4)(x+3)))
Please check me, but I'm not sure how you got to ((4)/((x+4)(x+3)))
... anyway, restrictions look good though.