Question

What is
`(1)/(x+2) +(6)/(x-5)` equal to?

Please show most of your work!!!

Thank you!!

Answer 1

`=(1)/(x+2)\cdot(x-5)/(x-5)+(6)/(x-5)\cdot(x+2)/(x+2)\\\\=(1(x-5)+6(x+2))/((x+2)(x-5))\\\\=(7x+7)/(x^(2)-3x-10)`

Usually, the "simplified" form has the polynomial multiplied out (as immediately above), rather than factored. If you want it factored, you can remove a factor of 7 from the terms of the numerator to get 7(x+1)/((x+2)(x-5)).