Solve x^2-x/x^2-2x-3divx^2-4x+3/1-x^2

$$\frac { x ^ { 2 } - x } { x ^ { 2 } - 2 x - 3 } \div \frac { x ^ { 2 } - 4 x + 3 } { 1 - x ^ { 2 } }$$

Evaluate

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

Short Solution Steps

Divide \frac{x^{2}-x}{x^{2}-2x-3} by \frac{x^{2}-4x+3}{1-x^{2}} by multiplying \frac{x^{2}-x}{x^{2}-2x-3} by the reciprocal of \frac{x^{2}-4x+3}{1-x^{2}}.

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

Factor the expressions that are not already factored.

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

Extract the negative sign in -1-x.

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

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

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

Expand the expression.

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

Expand

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

Short Solution Steps

Divide \frac{x^{2}-x}{x^{2}-2x-3} by \frac{x^{2}-4x+3}{1-x^{2}} by multiplying \frac{x^{2}-x}{x^{2}-2x-3} by the reciprocal of \frac{x^{2}-4x+3}{1-x^{2}}.

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

Factor the expressions that are not already factored.

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

Extract the negative sign in -1-x.

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

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

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

Expand the expression.

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