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

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

Evaluate

$$\frac{x^{4}-4x^{3}+6x^{2}-4x+2}{\left(x-1\right)^{4}}$$

Short Solution Steps

Factor the expressions that are not already factored.

$$\frac{\left(x-1\right)^{-2}\left(x^{4}-4x^{3}+6x^{2}-4x+2\right)}{\left(x-1\right)^{2}}$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\frac{x^{4}-4x^{3}+6x^{2}-4x+2}{\left(x-1\right)^{4}}$$

Expand the expression.

$$\frac{x^{4}-4x^{3}+6x^{2}-4x+2}{x^{4}-4x^{3}+6x^{2}-4x+1}$$

Expand

$$\frac{x^{4}-4x^{3}+6x^{2}-4x+2}{\left(x-1\right)^{4}}$$

Short Solution Steps

Factor the expressions that are not already factored.

$$\frac{\left(x-1\right)^{-2}\left(x^{4}-4x^{3}+6x^{2}-4x+2\right)}{\left(x-1\right)^{2}}$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\frac{x^{4}-4x^{3}+6x^{2}-4x+2}{\left(x-1\right)^{4}}$$

Expand the expression.

$$\frac{x^{4}-4x^{3}+6x^{2}-4x+2}{x^{4}-4x^{3}+6x^{2}-4x+1}$$