Pre-Algebra Examples

$\frac{3 x}{x - 6} + \frac{6 x}{4 x - 24}$

Step 1

Simplify each term.

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Step 1.1

Cancel the common factor of $6$ and $4 x - 24$ .

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Step 1.1.1

Factor $2$ out of $6 x$ .

$\frac{3 x}{x - 6} + \frac{2 (3 x)}{4 x - 24}$

Step 1.1.2

Cancel the common factors.

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Step 1.1.2.1

Factor $2$ out of $4 x$ .

$\frac{3 x}{x - 6} + \frac{2 (3 x)}{2 (2 x) - 24}$

Step 1.1.2.2

Factor $2$ out of $- 24$ .

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

Step 1.1.2.3

Factor $2$ out of $2 (2 x) + 2 (- 12)$ .

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

Step 1.1.2.4

Cancel the common factor.

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

Step 1.1.2.5

Rewrite the expression.

$\frac{3 x}{x - 6} + \frac{3 x}{2 x - 12}$

Step 1.2

Factor $2$ out of $2 x - 12$ .

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Step 1.2.1

Factor $2$ out of $2 x$ .

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

Step 1.2.2

Factor $2$ out of $- 12$ .

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

Step 1.2.3

Factor $2$ out of $2 x + 2 \cdot - 6$ .

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

Step 2

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

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

Step 3

Write each expression with a common denominator of $(x - 6) \cdot 2$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

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

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

Step 3.2

Reorder the factors of $(x - 6) \cdot 2$ .

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

Step 4

Combine the numerators over the common denominator.

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

Step 5

Simplify the numerator.

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Step 5.1

Factor $3 x$ out of $3 x \cdot 2 + 3 x$ .

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Step 5.1.1

Factor $3 x$ out of $3 x \cdot 2$ .

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

Step 5.1.2

Factor $3 x$ out of $3 x$ .

$\frac{3 x (2) + 3 x (1)}{2 (x - 6)}$

Step 5.1.3

Factor $3 x$ out of $3 x (2) + 3 x (1)$ .

$\frac{3 x (2 + 1)}{2 (x - 6)}$

Step 5.2

Add $2$ and $1$ .

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

Step 5.3

Multiply $3$ by $3$ .

$\frac{9 x}{2 (x - 6)}$