Basic Math Examples

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

Step 1

Multiply the numerator by the reciprocal of the denominator.

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

Step 2

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

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

Step 3

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

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

Step 4

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

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Step 4.1

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

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

Step 4.2

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

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

Step 4.3

Reorder the factors of $y \cdot 2$ .

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

Step 5

Combine the numerators over the common denominator.

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

Step 6

Cancel the common factor of $2$ .

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Step 6.1

Factor $2$ out of $2 y$ .

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

Step 6.2

Cancel the common factor.

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

Step 6.3

Rewrite the expression.

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

Step 7

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

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

Step 8

Cancel the common factor of $y - 2$ and $2 - y$ .

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Step 8.1

Factor $- 1$ out of $y$ .

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

Step 8.2

Rewrite $- 2$ as $- 1 (2)$ .

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

Step 8.3

Factor $- 1$ out of $- 1 (- y) - 1 (2)$ .

$\frac{- 1 (- y + 2)}{y (2 - y)}$

Step 8.4

Reorder terms.

$\frac{- 1 (- y + 2)}{y (- y + 2)}$

Step 8.5

Cancel the common factor.

$\frac{- 1 (- y + 2)}{y (- y + 2)}$

Step 8.6

Rewrite the expression.

$\frac{- 1}{y}$

Step 9

Move the negative in front of the fraction.

$- \frac{1}{y}$