To simplify the expression [tex]\(\frac{2n}{n+4} + \frac{7}{n-1}\)[/tex], we need to find a common denominator. The common denominator for the fractions is [tex]\((n+4)(n-1)\)[/tex].
1. Rewrite each fraction with the common denominator:
[tex]\[
\frac{2n}{n+4} = \frac{2n(n-1)}{(n+4)(n-1)}
\][/tex]
[tex]\[
\frac{7}{n-1} = \frac{7(n+4)}{(n+4)(n-1)}
\][/tex]
2. Add the two fractions:
[tex]\[
\frac{2n(n-1)}{(n+4)(n-1)} + \frac{7(n+4)}{(n+4)(n-1)} = \frac{2n(n-1) + 7(n+4)}{(n+4)(n-1)}
\][/tex]
3. Expand the numerators:
[tex]\[
2n(n-1) = 2n^2 - 2n
\][/tex]
[tex]\[
7(n+4) = 7n + 28
\][/tex]
4. Combine the expanded numerators:
[tex]\[
2n^2 - 2n + 7n + 28 = 2n^2 + 5n + 28
\][/tex]
5. Combine the fractions:
[tex]\[
\frac{2n^2 + 5n + 28}{(n+4)(n-1)}
\][/tex]
Thus, the expression [tex]\(\frac{2n}{n+4} + \frac{7}{n-1}\)[/tex] simplifies to [tex]\(\frac{2n^2 + 5n + 28}{(n+4)(n-1)}\)[/tex].
The correct answer is:
A. [tex]\(\frac{2n^2 + 5n + 28}{(n+4)(n-1)}\)[/tex]
