Basic Math Examples

$\frac{y}{3 y - 6} + \frac{3}{2 - y}$

Step 1

Factor $3$ out of $3 y - 6$ .

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Step 1.1

Factor $3$ out of $3 y$ .

$\frac{y}{3 (y) - 6} + \frac{3}{2 - y}$

Step 1.2

Factor $3$ out of $- 6$ .

$\frac{y}{3 y + 3 \cdot - 2} + \frac{3}{2 - y}$

Step 1.3

Factor $3$ out of $3 y + 3 \cdot - 2$ .

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

Step 2

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

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

Step 3

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

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

Step 4

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

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

Step 5

Simplify the expression.

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Step 5.1

Move a negative from the denominator of $\frac{3}{- 1 (- 2 + y)}$ to the numerator.

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

Step 5.2

Reorder terms.

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

Step 6

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

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

Step 7

Write each expression with a common denominator of $3 (y - 2)$ , by multiplying each by an appropriate factor of $1$ .

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Step 7.1

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

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

Step 7.2

Reorder the factors of $(y - 2) \cdot 3$ .

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

Step 8

Combine the numerators over the common denominator.

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

Step 9

Multiply $- 1 \cdot 3 \cdot 3$ .

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Step 9.1

Multiply $- 1$ by $3$ .

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

Step 9.2

Multiply $- 3$ by $3$ .

$\frac{y - 9}{3 (y - 2)}$