Solve x-2-x^2-5x/x-3/x+frac{3x{x-3}}

$$\frac { x - 2 - \frac { x ^ { 2 } - 5 x } { x - 3 } } { x + \frac { 3 x } { x - 3 } }$$

Evaluate

$$\frac{6}{x^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply x-2 times \frac{x-3}{x-3}.

$$\frac{\frac{\left(x-2\right)\left(x-3\right)}{x-3}-\frac{x^{2}-5x}{x-3}}{x+\frac{3x}{x-3}}$$

Since \frac{\left(x-2\right)\left(x-3\right)}{x-3} and \frac{x^{2}-5x}{x-3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{\left(x-2\right)\left(x-3\right)-\left(x^{2}-5x\right)}{x-3}}{x+\frac{3x}{x-3}}$$

Do the multiplications in \left(x-2\right)\left(x-3\right)-\left(x^{2}-5x\right).

$$\frac{\frac{x^{2}-3x-2x+6-x^{2}+5x}{x-3}}{x+\frac{3x}{x-3}}$$

Combine like terms in x^{2}-3x-2x+6-x^{2}+5x.

$$\frac{\frac{6}{x-3}}{x+\frac{3x}{x-3}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{x-3}{x-3}.

$$\frac{\frac{6}{x-3}}{\frac{x\left(x-3\right)}{x-3}+\frac{3x}{x-3}}$$

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

$$\frac{\frac{6}{x-3}}{\frac{x\left(x-3\right)+3x}{x-3}}$$

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

$$\frac{\frac{6}{x-3}}{\frac{x^{2}-3x+3x}{x-3}}$$

Combine like terms in x^{2}-3x+3x.

$$\frac{\frac{6}{x-3}}{\frac{x^{2}}{x-3}}$$

Divide \frac{6}{x-3} by \frac{x^{2}}{x-3} by multiplying \frac{6}{x-3} by the reciprocal of \frac{x^{2}}{x-3}.

$$\frac{6\left(x-3\right)}{\left(x-3\right)x^{2}}$$

Cancel out x-3 in both numerator and denominator.

$$\frac{6}{x^{2}}$$

Expand

$$\frac{6}{x^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply x-2 times \frac{x-3}{x-3}.

$$\frac{\frac{\left(x-2\right)\left(x-3\right)}{x-3}-\frac{x^{2}-5x}{x-3}}{x+\frac{3x}{x-3}}$$

Since \frac{\left(x-2\right)\left(x-3\right)}{x-3} and \frac{x^{2}-5x}{x-3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{\left(x-2\right)\left(x-3\right)-\left(x^{2}-5x\right)}{x-3}}{x+\frac{3x}{x-3}}$$

Do the multiplications in \left(x-2\right)\left(x-3\right)-\left(x^{2}-5x\right).

$$\frac{\frac{x^{2}-3x-2x+6-x^{2}+5x}{x-3}}{x+\frac{3x}{x-3}}$$

Combine like terms in x^{2}-3x-2x+6-x^{2}+5x.

$$\frac{\frac{6}{x-3}}{x+\frac{3x}{x-3}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{x-3}{x-3}.

$$\frac{\frac{6}{x-3}}{\frac{x\left(x-3\right)}{x-3}+\frac{3x}{x-3}}$$

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

$$\frac{\frac{6}{x-3}}{\frac{x\left(x-3\right)+3x}{x-3}}$$

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

$$\frac{\frac{6}{x-3}}{\frac{x^{2}-3x+3x}{x-3}}$$

Combine like terms in x^{2}-3x+3x.

$$\frac{\frac{6}{x-3}}{\frac{x^{2}}{x-3}}$$

Divide \frac{6}{x-3} by \frac{x^{2}}{x-3} by multiplying \frac{6}{x-3} by the reciprocal of \frac{x^{2}}{x-3}.

$$\frac{6\left(x-3\right)}{\left(x-3\right)x^{2}}$$

Cancel out x-3 in both numerator and denominator.

$$\frac{6}{x^{2}}$$