Algebra Examples

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

Step 1

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

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

Step 2

Simplify terms.

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Step 2.1

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

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

Step 2.2

Combine the numerators over the common denominator.

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

Step 3

Simplify the numerator.

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Step 3.1

Apply the distributive property.

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

Step 3.2

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

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Step 3.2.1

Move $x$ .

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

Step 3.2.2

Multiply $x$ by $x$ .

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

Step 3.3

Multiply $- 8$ by $- 1$ .

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

Step 3.4

Add $x$ and $8 x$ .

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

Step 3.5

Reorder terms.

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

Step 4

Simplify with factoring out.

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Step 4.1

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

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

Step 4.2

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

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

Step 4.3

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

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

Step 4.4

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

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

Step 4.5

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

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

Step 4.6

Simplify the expression.

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Step 4.6.1

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

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

Step 4.6.2

Move the negative in front of the fraction.

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