Solve 2n^2-11n-40/2n+16*14n+20/14n^2+55n+50

$$\frac { 2 n ^ { 2 } - 11 n - 40 } { 2 n + 16 } \cdot \frac { 14 n + 20 } { 14 n ^ { 2 } + 55 n + 50 }$$

Evaluate

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

Short Solution Steps

Factor the expressions that are not already factored in \frac{14n+20}{14n^{2}+55n+50}.

$$\frac{2n^{2}-11n-40}{2n+16}\times \frac{2\left(7n+10\right)}{\left(2n+5\right)\left(7n+10\right)}$$

Cancel out 7n+10 in both numerator and denominator.

$$\frac{2n^{2}-11n-40}{2n+16}\times \frac{2}{2n+5}$$

Multiply \frac{2n^{2}-11n-40}{2n+16} times \frac{2}{2n+5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(2n^{2}-11n-40\right)\times 2}{\left(2n+16\right)\left(2n+5\right)}$$

Factor the expressions that are not already factored.

$$\frac{2\left(n-8\right)\left(2n+5\right)}{2\left(n+8\right)\left(2n+5\right)}$$

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

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

Expand

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

Short Solution Steps

Factor the expressions that are not already factored in \frac{14n+20}{14n^{2}+55n+50}.

$$\frac{2n^{2}-11n-40}{2n+16}\times \frac{2\left(7n+10\right)}{\left(2n+5\right)\left(7n+10\right)}$$

Cancel out 7n+10 in both numerator and denominator.

$$\frac{2n^{2}-11n-40}{2n+16}\times \frac{2}{2n+5}$$

Multiply \frac{2n^{2}-11n-40}{2n+16} times \frac{2}{2n+5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(2n^{2}-11n-40\right)\times 2}{\left(2n+16\right)\left(2n+5\right)}$$

Factor the expressions that are not already factored.

$$\frac{2\left(n-8\right)\left(2n+5\right)}{2\left(n+8\right)\left(2n+5\right)}$$

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

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