Simplify 5/(x-1)-x/(x-8)

$\frac{5}{x - 1} - \frac{x}{x - 8}$

To write $\frac{5}{x - 1}$ as a fraction with a common denominator, multiply by $\frac{x - 8}{x - 8}$ .

$\frac{5}{x - 1} \cdot \frac{x - 8}{x - 8} - \frac{x}{x - 8}$

To write $- \frac{x}{x - 8}$ as a fraction with a common denominator, multiply by $\frac{x - 1}{x - 1}$ .

$\frac{5}{x - 1} \cdot \frac{x - 8}{x - 8} - \frac{x}{x - 8} \cdot \frac{x - 1}{x - 1}$

Write each expression with a common denominator of $(x - 1) (x - 8)$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{5}{x - 1}$ by $\frac{x - 8}{x - 8}$ .

$\frac{5 (x - 8)}{(x - 1) (x - 8)} - \frac{x}{x - 8} \cdot \frac{x - 1}{x - 1}$

Multiply $\frac{x}{x - 8}$ by $\frac{x - 1}{x - 1}$ .

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

Reorder the factors of $(x - 8) (x - 1)$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Apply the distributive property.

$\frac{5 x + 5 \cdot - 8 - x (x - 1)}{(x - 1) (x - 8)}$

Multiply $5$ by $- 8$ .

$\frac{5 x - 40 - x (x - 1)}{(x - 1) (x - 8)}$

Apply the distributive property.

$\frac{5 x - 40 - x \cdot x - x \cdot - 1}{(x - 1) (x - 8)}$

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

Move $x$ .

$\frac{5 x - 40 - (x \cdot x) - x \cdot - 1}{(x - 1) (x - 8)}$

Multiply $x$ by $x$ .

$\frac{5 x - 40 - x^{2} - x \cdot - 1}{(x - 1) (x - 8)}$

Multiply $- x \cdot - 1$ .

Multiply $- 1$ by $- 1$ .

$\frac{5 x - 40 - x^{2} + 1 x}{(x - 1) (x - 8)}$

Multiply $x$ by $1$ .

$\frac{5 x - 40 - x^{2} + x}{(x - 1) (x - 8)}$

Add $5 x$ and $x$ .

$\frac{6 x - 40 - x^{2}}{(x - 1) (x - 8)}$

Reorder terms.

$\frac{- x^{2} + 6 x - 40}{(x - 1) (x - 8)}$

Simplify with factoring out.

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

$\frac{- (x^{2}) + 6 x - 40}{(x - 1) (x - 8)}$

Factor $- 1$ out of $6 x$ .

$\frac{- (x^{2}) - (- 6 x) - 40}{(x - 1) (x - 8)}$

Factor $- 1$ out of $- (x^{2}) - (- 6 x)$ .

$\frac{- (x^{2} - 6 x) - 40}{(x - 1) (x - 8)}$

Rewrite $- 40$ as $- 1 (40)$ .

$\frac{- (x^{2} - 6 x) - 1 (40)}{(x - 1) (x - 8)}$

Factor $- 1$ out of $- (x^{2} - 6 x) - 1 (40)$ .

$\frac{- (x^{2} - 6 x + 40)}{(x - 1) (x - 8)}$

Simplify the expression.

Rewrite $- (x^{2} - 6 x + 40)$ as $- 1 (x^{2} - 6 x + 40)$ .

$\frac{- 1 (x^{2} - 6 x + 40)}{(x - 1) (x - 8)}$

Move the negative in front of the fraction.

$- \frac{x^{2} - 6 x + 40}{(x - 1) (x - 8)}$

Simplify 5/(x-1)-x/(x-8)

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