Simplify (x+5)/(x-8)-x

$\frac{x + 5}{x - 8} - x$

To write $- x$ as a fraction with a common denominator, multiply by $\frac{x - 8}{x - 8}$ .

$\frac{x + 5}{x - 8} - x \cdot \frac{x - 8}{x - 8}$

Simplify terms.

Combine $- x$ and $\frac{x - 8}{x - 8}$ .

$\frac{x + 5}{x - 8} + \frac{- x (x - 8)}{x - 8}$

Combine the numerators over the common denominator.

$\frac{x + 5 - x (x - 8)}{x - 8}$

Simplify the numerator.

Apply the distributive property.

$\frac{x + 5 - x \cdot x - x \cdot - 8}{x - 8}$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$\frac{x + 5 - (x \cdot x) - x \cdot - 8}{x - 8}$

Multiply $x$ by $x$ .

$\frac{x + 5 - x^{2} - x \cdot - 8}{x - 8}$

Multiply $- 8$ by $- 1$ .

$\frac{x + 5 - x^{2} + 8 x}{x - 8}$

Add $x$ and $8 x$ .

$\frac{9 x + 5 - x^{2}}{x - 8}$

Reorder terms.

$\frac{- x^{2} + 9 x + 5}{x - 8}$

Simplify with factoring out.

Factor $- 1$ out of $- x^{2}$ .

$\frac{- (x^{2}) + 9 x + 5}{x - 8}$

Factor $- 1$ out of $9 x$ .

$\frac{- (x^{2}) - (- 9 x) + 5}{x - 8}$

Factor $- 1$ out of $- (x^{2}) - (- 9 x)$ .

$\frac{- (x^{2} - 9 x) + 5}{x - 8}$

Rewrite $5$ as $- 1 (- 5)$ .

$\frac{- (x^{2} - 9 x) - 1 (- 5)}{x - 8}$

Factor $- 1$ out of $- (x^{2} - 9 x) - 1 (- 5)$ .

$\frac{- (x^{2} - 9 x - 5)}{x - 8}$

Simplify the expression.

Rewrite $- (x^{2} - 9 x - 5)$ as $- 1 (x^{2} - 9 x - 5)$ .

$\frac{- 1 (x^{2} - 9 x - 5)}{x - 8}$

Move the negative in front of the fraction.

$- \frac{x^{2} - 9 x - 5}{x - 8}$