Algebra Examples

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

Step 1

Factor $3$ out of $3 x - 6$ .

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Step 1.1

Factor $3$ out of $3 x$ .

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

Step 1.2

Factor $3$ out of $- 6$ .

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

Step 1.3

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

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

Step 2

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

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

Step 3

Write each expression with a common denominator of $3 (x - 2)$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

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

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

Step 3.2

Reorder the factors of $(x - 2) \cdot 3$ .

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

Step 4

Combine the numerators over the common denominator.

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

Step 5

Simplify the numerator.

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Step 5.1

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

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Step 5.1.1

Factor $x$ out of $2 x$ .

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

Step 5.1.2

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

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

Step 5.1.3

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

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

Step 5.2

Multiply $3$ by $3$ .

$\frac{x (2 + 9)}{3 (x - 2)}$

Step 5.3

Add $2$ and $9$ .

$\frac{x \cdot 11}{3 (x - 2)}$

Step 6

Move $11$ to the left of $x$ .

$\frac{11 x}{3 (x - 2)}$