Basic Math Examples

$\frac{2 y - 1}{y^{2} - 1} \div \frac{1 - 2 y}{y + 1}$

Step 1

To divide by a fraction, multiply by its reciprocal.

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

Step 2

Simplify the denominator.

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Step 2.1

Rewrite $1$ as $1^{2}$ .

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

Step 2.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = y$ and $b = 1$ .

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

Step 3

Simplify terms.

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Step 3.1

Cancel the common factor of $y + 1$ .

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Step 3.1.1

Cancel the common factor.

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

Step 3.1.2

Rewrite the expression.

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

Step 3.2

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

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

Step 3.3

Cancel the common factor of $2 y - 1$ and $1 - 2 y$ .

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Step 3.3.1

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

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

Step 3.3.2

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

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

Step 3.3.3

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

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

Step 3.3.4

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

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

Step 3.3.5

Reorder terms.

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

Step 3.3.6

Cancel the common factor.

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

Step 3.3.7

Rewrite the expression.

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

Step 3.4

Move the negative in front of the fraction.

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