Solve f(x)=1-1/(x-2)^2

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

Evaluate

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

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}}.

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

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

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

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

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

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

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

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

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

Expand

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

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}}.

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

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

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

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

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

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

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

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

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