Solve 2x^2-x-6/2x^2-3x-2*2x^2-5x-3/2x^2+11x+12

$$\frac { 2 x ^ { 2 } - x - 6 } { 2 x ^ { 2 } - 3 x - 2 } \cdot \frac { 2 x ^ { 2 } - 5 x - 3 } { 2 x ^ { 2 } + 11 x + 12 }$$

Evaluate

$$\frac{x-3}{x+4}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{2x^{2}-x-6}{2x^{2}-3x-2}.

$$\frac{\left(x-2\right)\left(2x+3\right)}{\left(x-2\right)\left(2x+1\right)}\times \frac{2x^{2}-5x-3}{2x^{2}+11x+12}$$

Cancel out x-2 in both numerator and denominator.

$$\frac{2x+3}{2x+1}\times \frac{2x^{2}-5x-3}{2x^{2}+11x+12}$$

Multiply \frac{2x+3}{2x+1} times \frac{2x^{2}-5x-3}{2x^{2}+11x+12} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(2x+3\right)\left(2x^{2}-5x-3\right)}{\left(2x+1\right)\left(2x^{2}+11x+12\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(x-3\right)\left(2x+1\right)\left(2x+3\right)}{\left(x+4\right)\left(2x+1\right)\left(2x+3\right)}$$

Cancel out \left(2x+1\right)\left(2x+3\right) in both numerator and denominator.

$$\frac{x-3}{x+4}$$

Expand

$$\frac{x-3}{x+4}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{2x^{2}-x-6}{2x^{2}-3x-2}.

$$\frac{\left(x-2\right)\left(2x+3\right)}{\left(x-2\right)\left(2x+1\right)}\times \frac{2x^{2}-5x-3}{2x^{2}+11x+12}$$

Cancel out x-2 in both numerator and denominator.

$$\frac{2x+3}{2x+1}\times \frac{2x^{2}-5x-3}{2x^{2}+11x+12}$$

Multiply \frac{2x+3}{2x+1} times \frac{2x^{2}-5x-3}{2x^{2}+11x+12} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(2x+3\right)\left(2x^{2}-5x-3\right)}{\left(2x+1\right)\left(2x^{2}+11x+12\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(x-3\right)\left(2x+1\right)\left(2x+3\right)}{\left(x+4\right)\left(2x+1\right)\left(2x+3\right)}$$

Cancel out \left(2x+1\right)\left(2x+3\right) in both numerator and denominator.

$$\frac{x-3}{x+4}$$