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

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

Evaluate

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

Short Solution Steps

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

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

Divide \frac{\left(x+2\right)\left(x^{2}-4x+4\right)}{\left(x^{2}-2x+1\right)\left(x-1\right)} by \frac{x^{2}-4}{x^{2}-1} by multiplying \frac{\left(x+2\right)\left(x^{2}-4x+4\right)}{\left(x^{2}-2x+1\right)\left(x-1\right)} by the reciprocal of \frac{x^{2}-4}{x^{2}-1}.

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

Factor the expressions that are not already factored in \frac{\left(x+2\right)\left(x^{2}-4x+4\right)\left(x^{2}-1\right)}{\left(x^{2}-2x+1\right)\left(x-1\right)\left(x^{2}-4\right)}.

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

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

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

Multiply \frac{\left(x-2\right)\left(x+1\right)}{\left(x-1\right)^{2}} times \frac{x-1}{x-2} by multiplying numerator times numerator and denominator times denominator.

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

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

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

Expand

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

Short Solution Steps

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

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

Divide \frac{\left(x+2\right)\left(x^{2}-4x+4\right)}{\left(x^{2}-2x+1\right)\left(x-1\right)} by \frac{x^{2}-4}{x^{2}-1} by multiplying \frac{\left(x+2\right)\left(x^{2}-4x+4\right)}{\left(x^{2}-2x+1\right)\left(x-1\right)} by the reciprocal of \frac{x^{2}-4}{x^{2}-1}.

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

Factor the expressions that are not already factored in \frac{\left(x+2\right)\left(x^{2}-4x+4\right)\left(x^{2}-1\right)}{\left(x^{2}-2x+1\right)\left(x-1\right)\left(x^{2}-4\right)}.

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

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

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

Multiply \frac{\left(x-2\right)\left(x+1\right)}{\left(x-1\right)^{2}} times \frac{x-1}{x-2} by multiplying numerator times numerator and denominator times denominator.

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

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

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