Question

How do you simplify `(x^2-4)/(x^2-7x+10) div (x^2+6x+5)/(x^2-25)`?

Answer 1

`(x+2)/(x+1)`

Explanation:

Rewrite
`(x^2-4)/(x^2-7+10)/(x^2+6x+5)/(x^2-25)`

Factor everything out
`((x+2)(x-2))/((x-5)(x-2))/((x+1)(x+5))/((x+5)(x-5))`

Cancel like terms
`(x+2)/(x-5)/(x+1)/(x-5)`

Dividing by a fraction is the same as multiplying buy the repciprocal
`(x+2)/(x-5)*(x-5)/(x+1)`

Cancel like terms
`(x+2)/1*1/(x+1)`

Multiply
`(x+2)/(x+1)`