Question

I need help with my pre-calculus homework, the image of the problem is attached. Directions: Complete the operations to write as a single rational expression

Answer 1

Given:

`(5)/(n-4)+(4n)/(n+1)`

To write as a single rational expression:

On cross multiplication we get,

`\begin{gathered} (5)/(n-4)+(4n)/(n+1)=(5(n+1)+4n(n-4))/((n-4)(n+1)) \\ =(5n+5+4n^2-16n)/((n-4)(n+1)) \\ =(4n^2-11n+5)/(n^2-4n+n-4) \\ =(4n^2-11n+5)/(n^2-3n-4) \end{gathered}`

Hence, the answer is,

`(4n^2-11n+5)/(n^2-3n-4)`