Algebra Examples

$\frac{2 x}{3} + \frac{x + 3}{3 x + 18}$

Step 1

Factor $3$ out of $3 x + 18$ .

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Step 1.1

Factor $3$ out of $3 x$ .

$\frac{2 x}{3} + \frac{x + 3}{3 (x) + 18}$

Step 1.2

Factor $3$ out of $18$ .

$\frac{2 x}{3} + \frac{x + 3}{3 x + 3 \cdot 6}$

Step 1.3

Factor $3$ out of $3 x + 3 \cdot 6$ .

$\frac{2 x}{3} + \frac{x + 3}{3 (x + 6)}$

Step 2

To write $\frac{2 x}{3}$ as a fraction with a common denominator, multiply by $\frac{x + 6}{x + 6}$ .

$\frac{2 x}{3} \cdot \frac{x + 6}{x + 6} + \frac{x + 3}{3 (x + 6)}$

Step 3

Simplify terms.

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Step 3.1

Multiply $\frac{2 x}{3}$ by $\frac{x + 6}{x + 6}$ .

$\frac{2 x (x + 6)}{3 (x + 6)} + \frac{x + 3}{3 (x + 6)}$

Step 3.2

Combine the numerators over the common denominator.

$\frac{2 x (x + 6) + x + 3}{3 (x + 6)}$

Step 4

Simplify the numerator.

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Step 4.1

Apply the distributive property.

$\frac{2 x \cdot x + 2 x \cdot 6 + x + 3}{3 (x + 6)}$

Step 4.2

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

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Step 4.2.1

Move $x$ .

$\frac{2 (x \cdot x) + 2 x \cdot 6 + x + 3}{3 (x + 6)}$

Step 4.2.2

Multiply $x$ by $x$ .

$\frac{2 x^{2} + 2 x \cdot 6 + x + 3}{3 (x + 6)}$

Step 4.3

Multiply $6$ by $2$ .

$\frac{2 x^{2} + 12 x + x + 3}{3 (x + 6)}$

Step 4.4

Add $12 x$ and $x$ .

$\frac{2 x^{2} + 13 x + 3}{3 (x + 6)}$