Solve n^2-5n-36/n^2-2n-24*6n-36/n^2-3n-54

$$\frac { n ^ { 2 } - 5 n - 36 } { n ^ { 2 } - 2 n - 24 } \cdot \frac { 6 n - 36 } { n ^ { 2 } - 3 n - 54 }$$

Evaluate

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

Short Solution Steps

Factor the expressions that are not already factored in \frac{n^{2}-5n-36}{n^{2}-2n-24}.

$$\frac{\left(n-9\right)\left(n+4\right)}{\left(n-6\right)\left(n+4\right)}\times \frac{6n-36}{n^{2}-3n-54}$$

Cancel out n+4 in both numerator and denominator.

$$\frac{n-9}{n-6}\times \frac{6n-36}{n^{2}-3n-54}$$

Multiply \frac{n-9}{n-6} times \frac{6n-36}{n^{2}-3n-54} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(n-9\right)\left(6n-36\right)}{\left(n-6\right)\left(n^{2}-3n-54\right)}$$

Factor the expressions that are not already factored.

$$\frac{6\left(n-9\right)\left(n-6\right)}{\left(n-9\right)\left(n-6\right)\left(n+6\right)}$$

Cancel out \left(n-9\right)\left(n-6\right) in both numerator and denominator.

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

Expand

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

Short Solution Steps

Factor the expressions that are not already factored in \frac{n^{2}-5n-36}{n^{2}-2n-24}.

$$\frac{\left(n-9\right)\left(n+4\right)}{\left(n-6\right)\left(n+4\right)}\times \frac{6n-36}{n^{2}-3n-54}$$

Cancel out n+4 in both numerator and denominator.

$$\frac{n-9}{n-6}\times \frac{6n-36}{n^{2}-3n-54}$$

Multiply \frac{n-9}{n-6} times \frac{6n-36}{n^{2}-3n-54} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(n-9\right)\left(6n-36\right)}{\left(n-6\right)\left(n^{2}-3n-54\right)}$$

Factor the expressions that are not already factored.

$$\frac{6\left(n-9\right)\left(n-6\right)}{\left(n-9\right)\left(n-6\right)\left(n+6\right)}$$

Cancel out \left(n-9\right)\left(n-6\right) in both numerator and denominator.

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