Question

How do you simplify `(x+6)/(x+7) - (x-7)/(x-6)`?

Answer 1

`13/(x^2+x-42)`

Explanation:

`(x+6)/(x+7)-(x-7)/(x-6)`

= `((x+6)(x-6)-(x-7)(x+7))/((x+7)(x-6))`

= `((x^2-36)-(x^2-49))/(x^2+7x-6x-42)`

= `(x^2-36-x^2+49)/(x^2+x-42)`

= `13/(x^2+x-42)`