Algebra Examples

$\frac{\frac{x}{4} + \frac{x}{3}}{\frac{x}{2}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

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

Step 2

To write $\frac{x}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$(\frac{x}{4} \cdot \frac{3}{3} + \frac{x}{3}) \frac{2}{x}$

Step 3

To write $\frac{x}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$(\frac{x}{4} \cdot \frac{3}{3} + \frac{x}{3} \cdot \frac{4}{4}) \frac{2}{x}$

Step 4

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{x}{4}$ by $\frac{3}{3}$ .

$(\frac{x \cdot 3}{4 \cdot 3} + \frac{x}{3} \cdot \frac{4}{4}) \frac{2}{x}$

Step 4.2

Multiply $4$ by $3$ .

$(\frac{x \cdot 3}{12} + \frac{x}{3} \cdot \frac{4}{4}) \frac{2}{x}$

Step 4.3

Multiply $\frac{x}{3}$ by $\frac{4}{4}$ .

$(\frac{x \cdot 3}{12} + \frac{x \cdot 4}{3 \cdot 4}) \frac{2}{x}$

Step 4.4

Multiply $3$ by $4$ .

$(\frac{x \cdot 3}{12} + \frac{x \cdot 4}{12}) \frac{2}{x}$

Step 5

Combine the numerators over the common denominator.

$\frac{x \cdot 3 + x \cdot 4}{12} \cdot \frac{2}{x}$

Step 6

Simplify the numerator.

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Step 6.1

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

$\frac{3 \cdot x + x \cdot 4}{12} \cdot \frac{2}{x}$

Step 6.2

Move $4$ to the left of $x$ .

$\frac{3 x + 4 \cdot x}{12} \cdot \frac{2}{x}$

Step 6.3

Add $3 x$ and $4 x$ .

$\frac{7 x}{12} \cdot \frac{2}{x}$

Step 7

Reduce the expression by cancelling the common factors.

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Step 7.1

Cancel the common factor of $x$ .

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Step 7.1.1

Factor $x$ out of $7 x$ .

$\frac{x \cdot 7}{12} \cdot \frac{2}{x}$

Step 7.1.2

Cancel the common factor.

$\frac{x \cdot 7}{12} \cdot \frac{2}{x}$

Step 7.1.3

Rewrite the expression.

$\frac{7}{12} \cdot 2$

Step 7.2

Cancel the common factor of $2$ .

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Step 7.2.1

Factor $2$ out of $12$ .

$\frac{7}{2 (6)} \cdot 2$

Step 7.2.2

Cancel the common factor.

$\frac{7}{2 \cdot 6} \cdot 2$

Step 7.2.3

Rewrite the expression.

$\frac{7}{6}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{7}{6}$

Decimal Form:

$1.1\overline{6}$

Mixed Number Form:

$1 \frac{1}{6}$