Question

Multiply and simplify: x^2-4/x^2-1 x+1/ x+2

Answer 1

2/(x-1) + x-11/(x^2+3x-4)
Factor the trinomial
2/(x-1) + x-11/(x-1)(x+4)
make the denominators the same by multiplying (x+4) on the left
2(x+4)/(x-1)(x+4) + x-11/(x-1)(x+4)
distribute the 2
2x+8+x-11/(x-1)(x+4)
combine like terms
3x-3/(x-1)(x+4)
remove the 3 from the top equation
3(x-1)/(x-1)(x+4) *note: 3(x-1) is the same as 3x-3
cancel (x-1) on the top and bottom
3/x+4 <---answer

Answer 2

an example for: Simplify fully: 2/(x-1) + x-11/(x^2+3x-4)?