Question

How do you simplify `\frac { \frac { p } { p + 2} + \frac { 12} { p + 5} } { \frac { p - 1} { p ^ { 2} + 7p + 10} }`?

Answer 1

Explained below

Explanation:

`(p/(p+2)+12/(p+5))/((p−1)/(p^2+7p+10))=((p(p+5)+12(p+2))/((p+2)*(p+5)))/((p−1)/((p+2)(p+5)))=(p^2+17p+24)/(p-1)`

It isn't possible to simplify in more. Maybe a bit differently written it could be this:
`p^2+17p+24=(p-1)(p+18)+42`