Question

What is the difference in simplest form?(n^2+10n+21) / (n^2+3n-28) - (3n)/(n-4)a) (2n+3)/(n-4)b) n/(n-4)c) (-2n+3)/(n-4)d) (4n+3)/(n-4)

Answer 1

Given the expression:

`(n^2+10n+21)/(n^2+3n-28)-(3n)/(n-4)`

We can express the quadratic polynomials as:

`\begin{gathered} n^2+10n+21=(n+3)(n+7) \\ n^2+3n-28=(n+7)(n-4) \end{gathered}`

Then:

`\begin{gathered} ((n+3)(n+7))/((n+7)(n-4))-(3n)/(n-4)=(n+3)/(n-4)-(3n)/(n-4) \\ \Rightarrow=(n+3-3n)/(n-4)=(-2n+3)/(n-4) \end{gathered}`