Question

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

Answer 1

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.