Pre-Algebra Examples

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

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Rewrite the division as a fraction.

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

Step 1.2

Multiply the numerator by the reciprocal of the denominator.

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

Step 1.3

Combine.

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

Step 1.4

Multiply $1$ by $1$ .

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

Step 1.5

Move $3$ to the left of $y^{2}$ .

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

Step 2

To write $9$ as a fraction with a common denominator, multiply by $\frac{3 y^{2}}{3 y^{2}}$ .

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

Step 3

Simplify terms.

Tap for more steps...

Step 3.1

Combine $9$ and $\frac{3 y^{2}}{3 y^{2}}$ .

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

Step 3.2

Combine the numerators over the common denominator.

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

Step 4

Multiply $9$ by $3$ .

$\frac{27 y^{2} - 1}{3 y^{2}} - \frac{1}{y}$

Step 5

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

$\frac{27 y^{2} - 1}{3 y^{2}} - \frac{1}{y} \cdot \frac{3 y}{3 y}$

Step 6

Write each expression with a common denominator of $3 y^{2}$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 6.1

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

$\frac{27 y^{2} - 1}{3 y^{2}} - \frac{3 y}{y (3 y)}$

Step 6.2

Raise $y$ to the power of $1$ .

$\frac{27 y^{2} - 1}{3 y^{2}} - \frac{3 y}{3 (y^{1} y)}$

Step 6.3

Raise $y$ to the power of $1$ .

$\frac{27 y^{2} - 1}{3 y^{2}} - \frac{3 y}{3 (y^{1} y^{1})}$

Step 6.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{27 y^{2} - 1}{3 y^{2}} - \frac{3 y}{3 y^{1 + 1}}$

Step 6.5

Add $1$ and $1$ .

$\frac{27 y^{2} - 1}{3 y^{2}} - \frac{3 y}{3 y^{2}}$

Step 7

Combine the numerators over the common denominator.

$\frac{27 y^{2} - 1 - 3 y}{3 y^{2}}$

Step 8

Reorder terms.

$\frac{27 y^{2} - 3 y - 1}{3 y^{2}}$