Solve x^2-x-6/2x^2+x-6*2x^2+15x-27/x^2-9

$$\frac { x ^ { 2 } - x - 6 } { 2 x ^ { 2 } + x - 6 } \cdot \frac { 2 x ^ { 2 } + 15 x - 27 } { x ^ { 2 } - 9 }$$

Evaluate

$$\frac{x+9}{x+3}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}-x-6}{2x^{2}+x-6}.

$$\frac{\left(x-3\right)\left(x+2\right)}{\left(2x-3\right)\left(x+2\right)}\times \frac{2x^{2}+15x-27}{x^{2}-9}$$

Cancel out x+2 in both numerator and denominator.

$$\frac{x-3}{2x-3}\times \frac{2x^{2}+15x-27}{x^{2}-9}$$

Multiply \frac{x-3}{2x-3} times \frac{2x^{2}+15x-27}{x^{2}-9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x-3\right)\left(2x^{2}+15x-27\right)}{\left(2x-3\right)\left(x^{2}-9\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(x-3\right)\left(2x-3\right)\left(x+9\right)}{\left(x-3\right)\left(2x-3\right)\left(x+3\right)}$$

Cancel out \left(x-3\right)\left(2x-3\right) in both numerator and denominator.

$$\frac{x+9}{x+3}$$

Expand

$$\frac{x+9}{x+3}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}-x-6}{2x^{2}+x-6}.

$$\frac{\left(x-3\right)\left(x+2\right)}{\left(2x-3\right)\left(x+2\right)}\times \frac{2x^{2}+15x-27}{x^{2}-9}$$

Cancel out x+2 in both numerator and denominator.

$$\frac{x-3}{2x-3}\times \frac{2x^{2}+15x-27}{x^{2}-9}$$

Multiply \frac{x-3}{2x-3} times \frac{2x^{2}+15x-27}{x^{2}-9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x-3\right)\left(2x^{2}+15x-27\right)}{\left(2x-3\right)\left(x^{2}-9\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(x-3\right)\left(2x-3\right)\left(x+9\right)}{\left(x-3\right)\left(2x-3\right)\left(x+3\right)}$$

Cancel out \left(x-3\right)\left(2x-3\right) in both numerator and denominator.

$$\frac{x+9}{x+3}$$