Solve 1/n-6divn+6/n^2+14n+48

$$\frac { 1 } { n - 6 } \div \frac { n + 6 } { n ^ { 2 } + 14 n + 48 }$$

Evaluate

$$\frac{n+8}{n-6}$$

Short Solution Steps

Divide \frac{1}{n-6} by \frac{n+6}{n^{2}+14n+48} by multiplying \frac{1}{n-6} by the reciprocal of \frac{n+6}{n^{2}+14n+48}.

$$\frac{n^{2}+14n+48}{\left(n-6\right)\left(n+6\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(n+6\right)\left(n+8\right)}{\left(n-6\right)\left(n+6\right)}$$

Cancel out n+6 in both numerator and denominator.

$$\frac{n+8}{n-6}$$

Expand

$$\frac{n+8}{n-6}$$

Short Solution Steps

Divide \frac{1}{n-6} by \frac{n+6}{n^{2}+14n+48} by multiplying \frac{1}{n-6} by the reciprocal of \frac{n+6}{n^{2}+14n+48}.

$$\frac{n^{2}+14n+48}{\left(n-6\right)\left(n+6\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(n+6\right)\left(n+8\right)}{\left(n-6\right)\left(n+6\right)}$$

Cancel out n+6 in both numerator and denominator.

$$\frac{n+8}{n-6}$$