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

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

Evaluate

$$\frac{x^{2}-4x+5}{\left(x-2\right)^{2}}$$

Short Solution Steps

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

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

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

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

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

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

Combine like terms in 1+x^{2}-4x+4.

$$\frac{5+x^{2}-4x}{\left(x-2\right)^{2}}$$

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

$$\frac{5+x^{2}-4x}{x^{2}-4x+4}$$

Expand

$$\frac{x^{2}-4x+5}{\left(x-2\right)^{2}}$$

Short Solution Steps

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

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

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

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

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

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

Combine like terms in 1+x^{2}-4x+4.

$$\frac{5+x^{2}-4x}{\left(x-2\right)^{2}}$$

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

$$\frac{5+x^{2}-4x}{x^{2}-4x+4}$$