Algebra Examples

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

Step 1

Multiply the numerator and denominator of the fraction by $3$ .

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Step 1.1

Multiply $\frac{\frac{x}{3} - 1}{x - 3}$ by $\frac{3}{3}$ .

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

Step 1.2

Combine.

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

Step 2

Apply the distributive property.

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

Step 3

Simplify terms.

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Step 3.1

Cancel the common factor of $3$ .

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Step 3.1.1

Cancel the common factor.

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

Step 3.1.2

Rewrite the expression.

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

Step 3.2

Multiply $3$ by $- 1$ .

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

Step 3.3

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

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Step 3.3.1

Factor $3$ out of $3 x$ .

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

Step 3.3.2

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

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

Step 3.3.3

Factor $3$ out of $3 (x) + 3 (- 3)$ .

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

Step 3.4

Cancel the common factor of $x - 3$ .

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Step 3.4.1

Cancel the common factor.

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

Step 3.4.2

Rewrite the expression.

$\frac{1}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{3}$

Decimal Form:

$0.\overline{3}$