Solve 1+3/(x-1)^2

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

Evaluate

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

Short Solution Steps

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

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

Since \frac{\left(x-1\right)^{2}}{\left(x-1\right)^{2}} and \frac{3}{\left(x-1\right)^{2}} have the same denominator, add them by adding their numerators.

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

Do the multiplications in \left(x-1\right)^{2}+3.

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

Combine like terms in x^{2}-2x+1+3.

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

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

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

Expand

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

Short Solution Steps

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

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

Since \frac{\left(x-1\right)^{2}}{\left(x-1\right)^{2}} and \frac{3}{\left(x-1\right)^{2}} have the same denominator, add them by adding their numerators.

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

Do the multiplications in \left(x-1\right)^{2}+3.

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

Combine like terms in x^{2}-2x+1+3.

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

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

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