Solve x^2-5x+6/x^2-2x-3*x^2-1/x^2-4

$$\frac { x ^ { 2 } - 5 x + 6 } { x ^ { 2 } - 2 x - 3 } \cdot \frac { x ^ { 2 } - 1 } { x ^ { 2 } - 4 }$$

Evaluate

$$\frac{x-1}{x+2}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}-5x+6}{x^{2}-2x-3}.

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

Cancel out x-3 in both numerator and denominator.

$$\frac{x-2}{x+1}\times \frac{x^{2}-1}{x^{2}-4}$$

Multiply \frac{x-2}{x+1} times \frac{x^{2}-1}{x^{2}-4} by multiplying numerator times numerator and denominator times denominator.

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

Factor the expressions that are not already factored.

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

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

$$\frac{x-1}{x+2}$$

Expand

$$\frac{x-1}{x+2}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}-5x+6}{x^{2}-2x-3}.

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

Cancel out x-3 in both numerator and denominator.

$$\frac{x-2}{x+1}\times \frac{x^{2}-1}{x^{2}-4}$$

Multiply \frac{x-2}{x+1} times \frac{x^{2}-1}{x^{2}-4} by multiplying numerator times numerator and denominator times denominator.

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

Factor the expressions that are not already factored.

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

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

$$\frac{x-1}{x+2}$$