Basic Math Examples

$\frac{y - 1}{y + 2} \div \frac{1 - y}{4 + y}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{y - 1}{y + 2} \cdot \frac{4 + y}{1 - y}$

Step 2

Multiply $\frac{y - 1}{y + 2}$ by $\frac{4 + y}{1 - y}$ .

$\frac{(y - 1) (4 + y)}{(y + 2) (1 - y)}$

Step 3

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

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Step 3.1

Factor $- 1$ out of $y$ .

$\frac{(- 1 (- y) - 1) (4 + y)}{(y + 2) (1 - y)}$

Step 3.2

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

$\frac{(- 1 (- y) - 1 (1)) (4 + y)}{(y + 2) (1 - y)}$

Step 3.3

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

$\frac{- 1 (- y + 1) (4 + y)}{(y + 2) (1 - y)}$

Step 3.4

Reorder terms.

$\frac{- 1 (- y + 1) (4 + y)}{(y + 2) (- y + 1)}$

Step 3.5

Cancel the common factor.

$\frac{- 1 (- y + 1) (4 + y)}{(y + 2) (- y + 1)}$

Step 3.6

Rewrite the expression.

$\frac{- 1 (4 + y)}{y + 2}$

Step 4

Move the negative in front of the fraction.

$- \frac{4 + y}{y + 2}$