Basic Math Examples

$\frac{3}{3 y - 9} + \frac{y - 2}{3 - y}$

Step 1

Simplify terms.

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Step 1.1

Cancel the common factor of $3$ and $3 y - 9$ .

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Step 1.1.1

Factor $3$ out of $3$ .

$\frac{3 \cdot 1}{3 y - 9} + \frac{y - 2}{3 - y}$

Step 1.1.2

Cancel the common factors.

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Step 1.1.2.1

Factor $3$ out of $3 y$ .

$\frac{3 \cdot 1}{3 (y) - 9} + \frac{y - 2}{3 - y}$

Step 1.1.2.2

Factor $3$ out of $- 9$ .

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

Step 1.1.2.3

Factor $3$ out of $3 (y) + 3 (- 3)$ .

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

Step 1.1.2.4

Cancel the common factor.

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

Step 1.1.2.5

Rewrite the expression.

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

Step 1.2

Rewrite $3$ as $- 1 (- 3)$ .

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

Step 1.3

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

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

Step 1.4

Factor $- 1$ out of $- 1 (- 3) - (y)$ .

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

Step 1.5

Simplify the expression.

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Step 1.5.1

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

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

Step 1.5.2

Reorder terms.

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

Step 1.6

Combine the numerators over the common denominator.

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

Step 2

Simplify the numerator.

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Step 2.1

Apply the distributive property.

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

Step 2.2

Multiply $- 1$ by $- 2$ .

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

Step 2.3

Add $1$ and $2$ .

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

Step 3

Cancel the common factor of $- y + 3$ and $y - 3$ .

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Step 3.1

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

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

Step 3.2

Rewrite $3$ as $- 1 (- 3)$ .

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

Step 3.3

Factor $- 1$ out of $- (y) - 1 (- 3)$ .

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

Step 3.4

Rewrite $- (y - 3)$ as $- 1 (y - 3)$ .

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

Step 3.5

Cancel the common factor.

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

Step 3.6

Divide $- 1$ by $1$ .

$- 1$