Solve x^2+3x-40/x^2+17x+72*x^2-81/x^2-25

$$\frac { x ^ { 2 } + 3 x - 40 } { x ^ { 2 } + 17 x + 72 } \cdot \frac { x ^ { 2 } - 81 } { x ^ { 2 } - 25 }$$

Evaluate

$$\frac{x-9}{x+5}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}+3x-40}{x^{2}+17x+72}.

$$\frac{\left(x-5\right)\left(x+8\right)}{\left(x+8\right)\left(x+9\right)}\times \frac{x^{2}-81}{x^{2}-25}$$

Cancel out x+8 in both numerator and denominator.

$$\frac{x-5}{x+9}\times \frac{x^{2}-81}{x^{2}-25}$$

Multiply \frac{x-5}{x+9} times \frac{x^{2}-81}{x^{2}-25} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x-5\right)\left(x^{2}-81\right)}{\left(x+9\right)\left(x^{2}-25\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(x-9\right)\left(x-5\right)\left(x+9\right)}{\left(x-5\right)\left(x+5\right)\left(x+9\right)}$$

Cancel out \left(x-5\right)\left(x+9\right) in both numerator and denominator.

$$\frac{x-9}{x+5}$$

Expand

$$\frac{x-9}{x+5}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}+3x-40}{x^{2}+17x+72}.

$$\frac{\left(x-5\right)\left(x+8\right)}{\left(x+8\right)\left(x+9\right)}\times \frac{x^{2}-81}{x^{2}-25}$$

Cancel out x+8 in both numerator and denominator.

$$\frac{x-5}{x+9}\times \frac{x^{2}-81}{x^{2}-25}$$

Multiply \frac{x-5}{x+9} times \frac{x^{2}-81}{x^{2}-25} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x-5\right)\left(x^{2}-81\right)}{\left(x+9\right)\left(x^{2}-25\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(x-9\right)\left(x-5\right)\left(x+9\right)}{\left(x-5\right)\left(x+5\right)\left(x+9\right)}$$

Cancel out \left(x-5\right)\left(x+9\right) in both numerator and denominator.

$$\frac{x-9}{x+5}$$