Solve left(x^2-2xright)^2/x-1-1/1-x

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

Evaluate

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

Short Solution Steps

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

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

Since \frac{\left(x^{2}-2x\right)^{2}}{x-1} and \frac{-1}{x-1} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in \left(x^{2}-2x\right)^{2}-\left(-1\right).

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

Expand

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

Short Solution Steps

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

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

Since \frac{\left(x^{2}-2x\right)^{2}}{x-1} and \frac{-1}{x-1} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in \left(x^{2}-2x\right)^{2}-\left(-1\right).

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