Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

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

Step 1.2

Combine $\frac{1}{3}$ and $x$ .

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

Step 1.3

Cancel the common factor of $3$ .

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Step 1.3.1

Factor $3$ out of $- 3$ .

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

Step 1.3.2

Cancel the common factor.

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

Step 1.3.3

Rewrite the expression.

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

Step 1.4

Apply the distributive property.

$\frac{x}{3} - 1 + \frac{2}{3} x + \frac{2}{3} \cdot 3$

Step 1.5

Combine $\frac{2}{3}$ and $x$ .

$\frac{x}{3} - 1 + \frac{2 x}{3} + \frac{2}{3} \cdot 3$

Step 1.6

Cancel the common factor of $3$ .

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Step 1.6.1

Cancel the common factor.

$\frac{x}{3} - 1 + \frac{2 x}{3} + \frac{2}{3} \cdot 3$

Step 1.6.2

Rewrite the expression.

$\frac{x}{3} - 1 + \frac{2 x}{3} + 2$

Step 2

Simplify terms.

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Step 2.1

Combine the numerators over the common denominator.

$- 1 + 2 + \frac{x + 2 x}{3}$

Step 2.2

Add $x$ and $2 x$ .

$- 1 + 2 + \frac{3 x}{3}$

Step 2.3

Cancel the common factor of $3$ .

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Step 2.3.1

Cancel the common factor.

$- 1 + 2 + \frac{3 x}{3}$

Step 2.3.2

Divide $x$ by $1$ .

$- 1 + 2 + x$

Step 2.4

Add $- 1$ and $2$ .

$1 + x$