Algebra Examples

$\frac{\frac{y}{2} - \frac{1}{x}}{\frac{6 y}{x}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$(\frac{y}{2} - \frac{1}{x}) \frac{x}{6 y}$

Step 2

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

$(\frac{y}{2} \cdot \frac{x}{x} - \frac{1}{x}) \frac{x}{6 y}$

Step 3

To write $- \frac{1}{x}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$(\frac{y}{2} \cdot \frac{x}{x} - \frac{1}{x} \cdot \frac{2}{2}) \frac{x}{6 y}$

Step 4

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

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Step 4.1

Multiply $\frac{y}{2}$ by $\frac{x}{x}$ .

$(\frac{y x}{2 x} - \frac{1}{x} \cdot \frac{2}{2}) \frac{x}{6 y}$

Step 4.2

Multiply $\frac{1}{x}$ by $\frac{2}{2}$ .

$(\frac{y x}{2 x} - \frac{2}{x \cdot 2}) \frac{x}{6 y}$

Step 4.3

Reorder the factors of $x \cdot 2$ .

$(\frac{y x}{2 x} - \frac{2}{2 x}) \frac{x}{6 y}$

Step 5

Combine the numerators over the common denominator.

$\frac{y x - 2}{2 x} \cdot \frac{x}{6 y}$

Step 6

Cancel the common factor of $x$ .

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Step 6.1

Factor $x$ out of $2 x$ .

$\frac{y x - 2}{x \cdot 2} \cdot \frac{x}{6 y}$

Step 6.2

Cancel the common factor.

$\frac{y x - 2}{x \cdot 2} \cdot \frac{x}{6 y}$

Step 6.3

Rewrite the expression.

$\frac{y x - 2}{2} \cdot \frac{1}{6 y}$

Step 7

Multiply $\frac{y x - 2}{2}$ by $\frac{1}{6 y}$ .

$\frac{y x - 2}{2 (6 y)}$

Step 8

Multiply $6$ by $2$ .

$\frac{y x - 2}{12 y}$