Pre-Algebra Examples

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

Step 1

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

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

Step 2

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

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

Step 3

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

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Step 3.1

Multiply $\frac{3}{y}$ by $\frac{3}{3}$ .

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

Step 3.2

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

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

Step 3.3

Reorder the factors of $y \cdot 3$ .

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

Step 4

Combine the numerators over the common denominator.

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

Step 5

Simplify the numerator.

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Step 5.1

Multiply $3$ by $3$ .

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

Step 5.2

Apply the distributive property.

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

Step 5.3

Multiply $- 1$ by $- 1$ .

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

Step 5.4

Apply the distributive property.

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

Step 5.5

Multiply $y$ by $y$ by adding the exponents.

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Step 5.5.1

Move $y$ .

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

Step 5.5.2

Multiply $y$ by $y$ .

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

Step 5.6

Multiply $y$ by $1$ .

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

Step 5.7

Reorder terms.

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

Step 6

Simplify with factoring out.

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Step 6.1

Factor $- 1$ out of $- y^{2}$ .

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

Step 6.2

Factor $- 1$ out of $y$ .

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

Step 6.3

Factor $- 1$ out of $- (y^{2}) - 1 (- y)$ .

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

Step 6.4

Rewrite $9$ as $- 1 (- 9)$ .

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

Step 6.5

Factor $- 1$ out of $- (y^{2} - y) - 1 (- 9)$ .

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

Step 6.6

Simplify the expression.

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Step 6.6.1

Rewrite $- (y^{2} - y - 9)$ as $- 1 (y^{2} - y - 9)$ .

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

Step 6.6.2

Move the negative in front of the fraction.

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