Solve (1-lambda/x-1)-x+1/x^2-x

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

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x-1}{x-1}.

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

Since \frac{x-1}{x-1} and \frac{\lambda }{x-1} have the same denominator, subtract them by subtracting their numerators.

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

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

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

Extract the negative sign in -x+1.

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

Cancel out x-1 in both numerator and denominator.

$$\frac{x-1-\lambda }{x-1}\times \frac{-1}{x}$$

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

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

Use the distributive property to multiply x-1-\lambda by -1.

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

Use the distributive property to multiply x-1 by x.

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

Expand

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x-1}{x-1}.

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

Since \frac{x-1}{x-1} and \frac{\lambda }{x-1} have the same denominator, subtract them by subtracting their numerators.

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

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

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

Extract the negative sign in -x+1.

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

Cancel out x-1 in both numerator and denominator.

$$\frac{x-1-\lambda }{x-1}\times \frac{-1}{x}$$

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

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

Use the distributive property to multiply x-1-\lambda by -1.

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

Use the distributive property to multiply x-1 by x.

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