Subtract. start fraction x squared minus 1 over x squared minus x minus 2 end fraction minus start fraction x minus 1 over x minus 2 end fraction

Question

(1 point)
Responses

1
1

0
0

–1
–1

start fraction x minus 1 over x minus 2 end fraction

Answer 1

= start fraction x squared - 1 over x squared - x - 2 end fraction - start fraction x - 1 over x - 2 end fraction
= start fraction (x + 1)(x - 1) over (x + 1)(x - 2) - (x - 1)(x - 2) end fraction
= start fraction (x + 1)(x - 1) - (x - 1)(x - 2) over (x + 1)(x - 2) end fraction
= start fraction x^2 + x - x - 1 - (x^2 - 2x - x + 2) over (x + 1)(x - 2) end fraction
= start fraction 2x + 1 - 2x + 2 over (x + 1)(x - 2) end fraction
= start fraction 3 over (x + 1)(x - 2) end fraction

So the answer is 3 over (x + 1)(x - 2)