Pre-Algebra Examples

$\frac{5 x + 2}{x} + \frac{2 x}{x + 6}$

Step 1

To write $\frac{5 x + 2}{x}$ as a fraction with a common denominator, multiply by $\frac{x + 6}{x + 6}$ .

$\frac{5 x + 2}{x} \cdot \frac{x + 6}{x + 6} + \frac{2 x}{x + 6}$

Step 2

To write $\frac{2 x}{x + 6}$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$\frac{5 x + 2}{x} \cdot \frac{x + 6}{x + 6} + \frac{2 x}{x + 6} \cdot \frac{x}{x}$

Step 3

Write each expression with a common denominator of $x (x + 6)$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{5 x + 2}{x}$ by $\frac{x + 6}{x + 6}$ .

$\frac{(5 x + 2) (x + 6)}{x (x + 6)} + \frac{2 x}{x + 6} \cdot \frac{x}{x}$

Step 3.2

Multiply $\frac{2 x}{x + 6}$ by $\frac{x}{x}$ .

$\frac{(5 x + 2) (x + 6)}{x (x + 6)} + \frac{2 x \cdot x}{(x + 6) x}$

Step 3.3

Reorder the factors of $(x + 6) x$ .

$\frac{(5 x + 2) (x + 6)}{x (x + 6)} + \frac{2 x \cdot x}{x (x + 6)}$

Step 4

Combine the numerators over the common denominator.

$\frac{(5 x + 2) (x + 6) + 2 x \cdot x}{x (x + 6)}$

Step 5

Simplify the numerator.

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Step 5.1

Expand $(5 x + 2) (x + 6)$ using the FOIL Method.

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Step 5.1.1

Apply the distributive property.

$\frac{5 x (x + 6) + 2 (x + 6) + 2 x \cdot x}{x (x + 6)}$

Step 5.1.2

Apply the distributive property.

$\frac{5 x \cdot x + 5 x \cdot 6 + 2 (x + 6) + 2 x \cdot x}{x (x + 6)}$

Step 5.1.3

Apply the distributive property.

$\frac{5 x \cdot x + 5 x \cdot 6 + 2 x + 2 \cdot 6 + 2 x \cdot x}{x (x + 6)}$

Step 5.2

Simplify and combine like terms.

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Step 5.2.1

Simplify each term.

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Step 5.2.1.1

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

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Step 5.2.1.1.1

Move $x$ .

$\frac{5 (x \cdot x) + 5 x \cdot 6 + 2 x + 2 \cdot 6 + 2 x \cdot x}{x (x + 6)}$

Step 5.2.1.1.2

Multiply $x$ by $x$ .

$\frac{5 x^{2} + 5 x \cdot 6 + 2 x + 2 \cdot 6 + 2 x \cdot x}{x (x + 6)}$

Step 5.2.1.2

Multiply $6$ by $5$ .

$\frac{5 x^{2} + 30 x + 2 x + 2 \cdot 6 + 2 x \cdot x}{x (x + 6)}$

Step 5.2.1.3

Multiply $2$ by $6$ .

$\frac{5 x^{2} + 30 x + 2 x + 12 + 2 x \cdot x}{x (x + 6)}$

Step 5.2.2

Add $30 x$ and $2 x$ .

$\frac{5 x^{2} + 32 x + 12 + 2 x \cdot x}{x (x + 6)}$

Step 5.3

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

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Step 5.3.1

Move $x$ .

$\frac{5 x^{2} + 32 x + 12 + 2 (x \cdot x)}{x (x + 6)}$

Step 5.3.2

Multiply $x$ by $x$ .

$\frac{5 x^{2} + 32 x + 12 + 2 x^{2}}{x (x + 6)}$

Step 5.4

Add $5 x^{2}$ and $2 x^{2}$ .

$\frac{7 x^{2} + 32 x + 12}{x (x + 6)}$