Algebra Examples

$\frac{7 x + 2}{x - 8} + 5 x$

Step 1

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

$\frac{7 x + 2}{x - 8} + \frac{5 x (x - 8)}{x - 8}$

Step 2

Combine the numerators over the common denominator.

$\frac{7 x + 2 + 5 x (x - 8)}{x - 8}$

Step 3

Simplify the numerator.

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Step 3.1

Apply the distributive property.

$\frac{7 x + 2 + 5 x \cdot x + 5 x \cdot - 8}{x - 8}$

Step 3.2

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

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Step 3.2.1

Move $x$ .

$\frac{7 x + 2 + 5 (x \cdot x) + 5 x \cdot - 8}{x - 8}$

Step 3.2.2

Multiply $x$ by $x$ .

$\frac{7 x + 2 + 5 x^{2} + 5 x \cdot - 8}{x - 8}$

Step 3.3

Multiply $- 8$ by $5$ .

$\frac{7 x + 2 + 5 x^{2} - 40 x}{x - 8}$

Step 3.4

Subtract $40 x$ from $7 x$ .

$\frac{- 33 x + 2 + 5 x^{2}}{x - 8}$

Step 3.5

Reorder terms.

$\frac{5 x^{2} - 33 x + 2}{x - 8}$