Solve 3n/n+3+5/n-4

$$\frac { 3 n } { n + 3 } + \frac { 5 } { n - 4 }$$

Evaluate

$$\frac{3n^{2}-7n+15}{\left(n-4\right)\left(n+3\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of n+3 and n-4 is \left(n-4\right)\left(n+3\right). Multiply \frac{3n}{n+3} times \frac{n-4}{n-4}. Multiply \frac{5}{n-4} times \frac{n+3}{n+3}.

$$\frac{3n\left(n-4\right)}{\left(n-4\right)\left(n+3\right)}+\frac{5\left(n+3\right)}{\left(n-4\right)\left(n+3\right)}$$

Since \frac{3n\left(n-4\right)}{\left(n-4\right)\left(n+3\right)} and \frac{5\left(n+3\right)}{\left(n-4\right)\left(n+3\right)} have the same denominator, add them by adding their numerators.

$$\frac{3n\left(n-4\right)+5\left(n+3\right)}{\left(n-4\right)\left(n+3\right)}$$

Do the multiplications in 3n\left(n-4\right)+5\left(n+3\right).

$$\frac{3n^{2}-12n+5n+15}{\left(n-4\right)\left(n+3\right)}$$

Combine like terms in 3n^{2}-12n+5n+15.

$$\frac{3n^{2}-7n+15}{\left(n-4\right)\left(n+3\right)}$$

Expand \left(n-4\right)\left(n+3\right).

$$\frac{3n^{2}-7n+15}{n^{2}-n-12}$$

Differentiate w.r.t. n

$$\frac{4n^{2}-102n+99}{n^{4}-2n^{3}-23n^{2}+24n+144}$$