Basic Math Examples

$\frac{1}{b^{2}} - \frac{1}{y^{2}} \div \frac{1}{b} - \frac{1}{y}$

Step 1

Simplify each term.

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Step 1.1

To divide by a fraction, multiply by its reciprocal.

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

Step 1.2

Combine $\frac{1}{y^{2}}$ and $b$ .

$\frac{1}{b^{2}} - \frac{b}{y^{2}} - \frac{1}{y}$

Step 2

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

$\frac{1}{b^{2}} \cdot \frac{y^{2}}{y^{2}} - \frac{b}{y^{2}} - \frac{1}{y}$

Step 3

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

$\frac{1}{b^{2}} \cdot \frac{y^{2}}{y^{2}} - \frac{b}{y^{2}} \cdot \frac{b^{2}}{b^{2}} - \frac{1}{y}$

Step 4

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

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Step 4.1

Multiply $\frac{1}{b^{2}}$ by $\frac{y^{2}}{y^{2}}$ .

$\frac{y^{2}}{b^{2} y^{2}} - \frac{b}{y^{2}} \cdot \frac{b^{2}}{b^{2}} - \frac{1}{y}$

Step 4.2

Multiply $\frac{b}{y^{2}}$ by $\frac{b^{2}}{b^{2}}$ .

$\frac{y^{2}}{b^{2} y^{2}} - \frac{b \cdot b^{2}}{y^{2} b^{2}} - \frac{1}{y}$

Step 4.3

Reorder the factors of $y^{2} b^{2}$ .

$\frac{y^{2}}{b^{2} y^{2}} - \frac{b \cdot b^{2}}{b^{2} y^{2}} - \frac{1}{y}$

Step 5

Combine the numerators over the common denominator.

$\frac{y^{2} - b \cdot b^{2}}{b^{2} y^{2}} - \frac{1}{y}$

Step 6

Multiply $b$ by $b^{2}$ by adding the exponents.

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Step 6.1

Move $b^{2}$ .

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

Step 6.2

Multiply $b^{2}$ by $b$ .

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Step 6.2.1

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

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

Step 6.2.2

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

$\frac{y^{2} - b^{2 + 1}}{b^{2} y^{2}} - \frac{1}{y}$

Step 6.3

Add $2$ and $1$ .

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

Step 7

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

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

Step 8

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

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Step 8.1

Multiply $\frac{1}{y}$ by $\frac{b^{2} y}{b^{2} y}$ .

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

Step 8.2

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

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

Step 8.3

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

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

Step 8.4

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

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

Step 8.5

Add $1$ and $1$ .

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

Step 9

Combine the numerators over the common denominator.

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