Algebra Examples

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

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

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

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

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

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

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Multiply $\frac{2}{y + 3}$ and $\frac{3}{3}$ .

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

Multiply $\frac{1}{3}$ and $\frac{y + 3}{y + 3}$ .

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

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

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Multiply $2$ by $3$ .

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

Apply the distributive property.

$\frac{6 - y - 1 \cdot 3}{3 (y + 3)}$

Multiply $- 1$ by $3$ .

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

Subtract $3$ from $6$ .

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

Simplify with factoring out.

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

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

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

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

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

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

Simplify the expression.

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

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

Move the negative in front of the fraction.

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

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