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

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

Evaluate

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

Short Solution Steps

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

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

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

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

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

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

Combine like terms in 1-x+2.

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

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

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

Expand

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

Short Solution Steps

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

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

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

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

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

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

Combine like terms in 1-x+2.

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

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

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