Basic Math Examples

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

Step 1

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

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

Step 2

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

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

Step 3

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

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

Step 4

Reorder terms.

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

Step 5

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

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

Step 6

Write each expression with a common denominator of $(y - 1) \cdot - 1$ , by multiplying each by an appropriate factor of $1$ .

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Step 6.1

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

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

Step 6.2

Reorder the factors of $(y - 1) \cdot - 1$ .

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

Step 7

Combine the numerators over the common denominator.

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

Step 8

Simplify the numerator.

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Step 8.1

Move $- 1$ to the left of $y$ .

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

Step 8.2

Rewrite $- 1 y$ as $- y$ .

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

Step 9

Simplify with factoring out.

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Step 9.1

Move the negative in front of the fraction.

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

Step 9.2

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

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

Step 9.3

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

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

Step 9.4

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

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

Step 9.5

Simplify the expression.

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Step 9.5.1

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

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

Step 9.5.2

Move the negative in front of the fraction.

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

Step 9.5.3

Multiply $- 1$ by $- 1$ .

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

Step 9.5.4

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

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