Solve (x-x+5/x-3)div1/x-3

$$(x- \frac{ x+5 }{ x-3 } ) \div \frac{ 1 }{ x-3 }$$

Evaluate

$$\left(x-5\right)\left(x+1\right)$$

Short Solution Steps

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

$$\frac{\frac{x\left(x-3\right)}{x-3}-\frac{x+5}{x-3}}{\frac{1}{x-3}}$$

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

$$\frac{\frac{x\left(x-3\right)-\left(x+5\right)}{x-3}}{\frac{1}{x-3}}$$

Do the multiplications in x\left(x-3\right)-\left(x+5\right).

$$\frac{\frac{x^{2}-3x-x-5}{x-3}}{\frac{1}{x-3}}$$

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

$$\frac{\frac{x^{2}-4x-5}{x-3}}{\frac{1}{x-3}}$$

Divide \frac{x^{2}-4x-5}{x-3} by \frac{1}{x-3} by multiplying \frac{x^{2}-4x-5}{x-3} by the reciprocal of \frac{1}{x-3}.

$$\frac{\left(x^{2}-4x-5\right)\left(x-3\right)}{x-3}$$

Cancel out x-3 in both numerator and denominator.

$$x^{2}-4x-5$$

Expand

$$x^{2}-4x-5$$

Short Solution Steps

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

$$\frac{\frac{x\left(x-3\right)}{x-3}-\frac{x+5}{x-3}}{\frac{1}{x-3}}$$

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

$$\frac{\frac{x\left(x-3\right)-\left(x+5\right)}{x-3}}{\frac{1}{x-3}}$$

Do the multiplications in x\left(x-3\right)-\left(x+5\right).

$$\frac{\frac{x^{2}-3x-x-5}{x-3}}{\frac{1}{x-3}}$$

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

$$\frac{\frac{x^{2}-4x-5}{x-3}}{\frac{1}{x-3}}$$

Divide \frac{x^{2}-4x-5}{x-3} by \frac{1}{x-3} by multiplying \frac{x^{2}-4x-5}{x-3} by the reciprocal of \frac{1}{x-3}.

$$\frac{\left(x^{2}-4x-5\right)\left(x-3\right)}{x-3}$$

Cancel out x-3 in both numerator and denominator.

$$x^{2}-4x-5$$