Solve (n-9)/(n+5)(n+2)*(n-4)(n+2)/(n-9)

$$\frac { ( n - 9 ) } { ( n + 5 ) ( n + 2 ) } \cdot \frac { ( n - 4 ) ( n + 2 ) } { ( n - 9 ) }$$

Evaluate

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

Short Solution Steps

Apply the distributive property by multiplying each term of n+5 by each term of n+2.

$$\frac{n-9}{n^{2}+2n+5n+10}\times \frac{\left(n-4\right)\left(n+2\right)}{n-9}$$

Combine 2n and 5n to get 7n.

$$\frac{n-9}{n^{2}+7n+10}\times \frac{\left(n-4\right)\left(n+2\right)}{n-9}$$

Apply the distributive property by multiplying each term of n-4 by each term of n+2.

$$\frac{n-9}{n^{2}+7n+10}\times \frac{n^{2}+2n-4n-8}{n-9}$$

Combine 2n and -4n to get -2n.

$$\frac{n-9}{n^{2}+7n+10}\times \frac{n^{2}-2n-8}{n-9}$$

Multiply \frac{n-9}{n^{2}+7n+10} times \frac{n^{2}-2n-8}{n-9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(n-9\right)\left(n^{2}-2n-8\right)}{\left(n^{2}+7n+10\right)\left(n-9\right)}$$

Cancel out n-9 in both numerator and denominator.

$$\frac{n^{2}-2n-8}{n^{2}+7n+10}$$

Factor the expressions that are not already factored.

$$\frac{\left(n-4\right)\left(n+2\right)}{\left(n+2\right)\left(n+5\right)}$$

Cancel out n+2 in both numerator and denominator.

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

Expand

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

Short Solution Steps

Apply the distributive property by multiplying each term of n+5 by each term of n+2.

$$\frac{n-9}{n^{2}+2n+5n+10}\times \frac{\left(n-4\right)\left(n+2\right)}{n-9}$$

Combine 2n and 5n to get 7n.

$$\frac{n-9}{n^{2}+7n+10}\times \frac{\left(n-4\right)\left(n+2\right)}{n-9}$$

Apply the distributive property by multiplying each term of n-4 by each term of n+2.

$$\frac{n-9}{n^{2}+7n+10}\times \frac{n^{2}+2n-4n-8}{n-9}$$

Combine 2n and -4n to get -2n.

$$\frac{n-9}{n^{2}+7n+10}\times \frac{n^{2}-2n-8}{n-9}$$

Multiply \frac{n-9}{n^{2}+7n+10} times \frac{n^{2}-2n-8}{n-9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(n-9\right)\left(n^{2}-2n-8\right)}{\left(n^{2}+7n+10\right)\left(n-9\right)}$$

Cancel out n-9 in both numerator and denominator.

$$\frac{n^{2}-2n-8}{n^{2}+7n+10}$$

Factor the expressions that are not already factored.

$$\frac{\left(n-4\right)\left(n+2\right)}{\left(n+2\right)\left(n+5\right)}$$

Cancel out n+2 in both numerator and denominator.

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