Solve x^2/y-1*x^2-2x+1/x^2-xdivx^3-x/(y-1)-x/1-y

$$\frac { x ^ { 2 } } { y - 1 } \times \frac { x ^ { 2 } - 2 x + 1 } { x ^ { 2 } - x } \div \frac { x ^ { 3 } - x } { ( y - 1 ) - x / 1 - y }$$

Evaluate

$$-\frac{1}{y-1}$$

Short Solution Steps

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

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

Cancel out x-1 in both numerator and denominator.

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

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

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

Cancel out x in both numerator and denominator.

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

Anything divided by one gives itself.

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

Combine y and -y to get 0.

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

Factor the expressions that are not already factored in \frac{x^{3}-x}{-1-x}.

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

Extract the negative sign in 1+x.

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

Cancel out -x-1 in both numerator and denominator.

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

Expand the expression.

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

Express \frac{\frac{x\left(x-1\right)}{y-1}}{-x^{2}+x} as a single fraction.

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

Factor the expressions that are not already factored.

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

Extract the negative sign in -1+x.

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

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

$$\frac{-1}{y-1}$$

Expand

$$-\frac{1}{y-1}$$

Short Solution Steps

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

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

Cancel out x-1 in both numerator and denominator.

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

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

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

Cancel out x in both numerator and denominator.

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

Anything divided by one gives itself.

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

Combine y and -y to get 0.

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

Factor the expressions that are not already factored in \frac{x^{3}-x}{-1-x}.

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

Extract the negative sign in 1+x.

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

Cancel out -x-1 in both numerator and denominator.

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

Expand the expression.

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

Express \frac{\frac{x\left(x-1\right)}{y-1}}{-x^{2}+x} as a single fraction.

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

Factor the expressions that are not already factored.

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

Extract the negative sign in -1+x.

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

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

$$\frac{-1}{y-1}$$