Solve n^2+3n+2/5n+10div6n^2+6n/5n-5

$$\frac { n ^ { 2 } + 3 n + 2 } { 5 n + 10 } \div \frac { 6 n ^ { 2 } + 6 n } { 5 n - 5 }$$

Evaluate

$$\frac{1}{6}-\frac{1}{6n}$$

Short Solution Steps

Divide \frac{n^{2}+3n+2}{5n+10} by \frac{6n^{2}+6n}{5n-5} by multiplying \frac{n^{2}+3n+2}{5n+10} by the reciprocal of \frac{6n^{2}+6n}{5n-5}.

$$\frac{\left(n^{2}+3n+2\right)\left(5n-5\right)}{\left(5n+10\right)\left(6n^{2}+6n\right)}$$

Factor the expressions that are not already factored.

$$\frac{5\left(n-1\right)\left(n+1\right)\left(n+2\right)}{5\times 6n\left(n+1\right)\left(n+2\right)}$$

Cancel out 5\left(n+1\right)\left(n+2\right) in both numerator and denominator.

$$\frac{n-1}{6n}$$

Expand

$$\frac{1}{6}-\frac{1}{6n}$$

Short Solution Steps

Divide \frac{n^{2}+3n+2}{5n+10} by \frac{6n^{2}+6n}{5n-5} by multiplying \frac{n^{2}+3n+2}{5n+10} by the reciprocal of \frac{6n^{2}+6n}{5n-5}.

$$\frac{\left(n^{2}+3n+2\right)\left(5n-5\right)}{\left(5n+10\right)\left(6n^{2}+6n\right)}$$

Factor the expressions that are not already factored.

$$\frac{5\left(n-1\right)\left(n+1\right)\left(n+2\right)}{5\times 6n\left(n+1\right)\left(n+2\right)}$$

Cancel out 5\left(n+1\right)\left(n+2\right) in both numerator and denominator.

$$\frac{n-1}{6n}$$