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

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

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x-3\right)^{2} and x-3 is \left(x-3\right)^{2}. Multiply \frac{1}{x-3} times \frac{x-3}{x-3}.

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

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

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

Do the multiplications in 1-\left(x-3\right).

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

Combine like terms in 1-x+3.

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

Expand \left(x-3\right)^{2}.

$$\frac{4-x}{x^{2}-6x+9}$$

Expand

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x-3\right)^{2} and x-3 is \left(x-3\right)^{2}. Multiply \frac{1}{x-3} times \frac{x-3}{x-3}.

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

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

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

Do the multiplications in 1-\left(x-3\right).

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

Combine like terms in 1-x+3.

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

Expand \left(x-3\right)^{2}.

$$\frac{4-x}{x^{2}-6x+9}$$