Solve 1-x^2/2x-2*2x+2/2x^2-x-3

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

Evaluate

$$-\frac{x+1}{2x-3}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{1-x^{2}}{2x-2}.

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

Cancel out x-1 in both numerator and denominator.

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

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

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

Cancel out x+1 in both numerator and denominator.

$$\frac{-x-1}{2}\times \frac{2}{2x-3}$$

Multiply \frac{-x-1}{2} times \frac{2}{2x-3} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out 2 in both numerator and denominator.

$$\frac{-x-1}{2x-3}$$

Expand

$$-\frac{x+1}{2x-3}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{1-x^{2}}{2x-2}.

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

Cancel out x-1 in both numerator and denominator.

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

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

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

Cancel out x+1 in both numerator and denominator.

$$\frac{-x-1}{2}\times \frac{2}{2x-3}$$

Multiply \frac{-x-1}{2} times \frac{2}{2x-3} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out 2 in both numerator and denominator.

$$\frac{-x-1}{2x-3}$$