Basic Math Examples

$\frac{y + 3}{y - 1} + \frac{y + 5}{2 - 2 y}$

Step 1

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

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Step 1.1

Factor $2$ out of $2$ .

$\frac{y + 3}{y - 1} + \frac{y + 5}{2 (1) - 2 y}$

Step 1.2

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

$\frac{y + 3}{y - 1} + \frac{y + 5}{2 (1) + 2 (- y)}$

Step 1.3

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

$\frac{y + 3}{y - 1} + \frac{y + 5}{2 (1 - y)}$

Step 2

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

$\frac{y + 3}{y - 1} + \frac{y + 5}{2 (- 1 (- 1) - y)}$

Step 3

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

$\frac{y + 3}{y - 1} + \frac{y + 5}{2 (- 1 (- 1) - (y))}$

Step 4

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

$\frac{y + 3}{y - 1} + \frac{y + 5}{2 (- 1 (- 1 + y))}$

Step 5

Simplify the expression.

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Step 5.1

Move a negative from the denominator of $\frac{y + 5}{2 (- 1 (- 1 + y))}$ to the numerator.

$\frac{y + 3}{y - 1} + \frac{- (y + 5)}{2 (- 1 + y)}$

Step 5.2

Reorder terms.

$\frac{y + 3}{y - 1} + \frac{- (y + 5)}{2 (y - 1)}$

Step 6

To write $\frac{y + 3}{y - 1}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{y + 3}{y - 1} \cdot \frac{2}{2} + \frac{- (y + 5)}{2 (y - 1)}$

Step 7

Write each expression with a common denominator of $(y - 1) \cdot 2$ , by multiplying each by an appropriate factor of $1$ .

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Step 7.1

Multiply $\frac{y + 3}{y - 1}$ by $\frac{2}{2}$ .

$\frac{(y + 3) \cdot 2}{(y - 1) \cdot 2} + \frac{- (y + 5)}{2 (y - 1)}$

Step 7.2

Reorder the factors of $(y - 1) \cdot 2$ .

$\frac{(y + 3) \cdot 2}{2 (y - 1)} + \frac{- (y + 5)}{2 (y - 1)}$

Step 8

Combine the numerators over the common denominator.

$\frac{(y + 3) \cdot 2 - (y + 5)}{2 (y - 1)}$

Step 9

Simplify the numerator.

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Step 9.1

Apply the distributive property.

$\frac{y \cdot 2 + 3 \cdot 2 - (y + 5)}{2 (y - 1)}$

Step 9.2

Move $2$ to the left of $y$ .

$\frac{2 \cdot y + 3 \cdot 2 - (y + 5)}{2 (y - 1)}$

Step 9.3

Multiply $3$ by $2$ .

$\frac{2 \cdot y + 6 - (y + 5)}{2 (y - 1)}$

Step 9.4

Apply the distributive property.

$\frac{2 y + 6 - y - 1 \cdot 5}{2 (y - 1)}$

Step 9.5

Multiply $- 1$ by $5$ .

$\frac{2 y + 6 - y - 5}{2 (y - 1)}$

Step 9.6

Subtract $y$ from $2 y$ .

$\frac{y + 6 - 5}{2 (y - 1)}$

Step 9.7

Subtract $5$ from $6$ .

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