Pre-Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

Factor $3$ out of $3 a$ .

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

Step 1.1.2

Factor $3$ out of $- 6$ .

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

Step 1.1.3

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

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

Step 1.2

Cancel the common factor of $a - 2$ .

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Step 1.2.1

Cancel the common factor.

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

Step 1.2.2

Rewrite the expression.

$\frac{1}{3} + \frac{2 a}{2}$

Step 1.3

Cancel the common factor of $2$ .

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Step 1.3.1

Cancel the common factor.

$\frac{1}{3} + \frac{2 a}{2}$

Step 1.3.2

Divide $a$ by $1$ .

$\frac{1}{3} + a$

Step 2

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

$\frac{1}{3} + a \cdot \frac{3}{3}$

Step 3

Simplify terms.

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Step 3.1

Combine $a$ and $\frac{3}{3}$ .

$\frac{1}{3} + \frac{a \cdot 3}{3}$

Step 3.2

Combine the numerators over the common denominator.

$\frac{1 + a \cdot 3}{3}$

Step 4

Move $3$ to the left of $a$ .

$\frac{1 + 3 a}{3}$