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

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

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{\left(x-1\right)^{2}}{\left(x-1\right)^{2}}.

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

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

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

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

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

Expand \left(x-1\right)^{2}.

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

Expand

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{\left(x-1\right)^{2}}{\left(x-1\right)^{2}}.

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

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

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

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

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

Expand \left(x-1\right)^{2}.

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