Solve x-3/x^2-3x+2/x-3

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

Evaluate

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

Short Solution Steps

Factor the expressions that are not already factored in \frac{x-3}{x^{2}-3x}.

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

Cancel out x-3 in both numerator and denominator.

$$\frac{1}{x}+\frac{2}{x-3}$$

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

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

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

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

Combine like terms in x-3+2x.

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

Expand x\left(x-3\right).

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

Expand

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

Short Solution Steps

Factor the expressions that are not already factored in \frac{x-3}{x^{2}-3x}.

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

Cancel out x-3 in both numerator and denominator.

$$\frac{1}{x}+\frac{2}{x-3}$$

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

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

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

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

Combine like terms in x-3+2x.

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

Expand x\left(x-3\right).

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