Basic Math Examples

$1 + \frac{4}{b} + \frac{4}{b^{2}} \div 1 - \frac{6}{b} - \frac{16}{b^{2}}$

Step 1

Combine fractions.

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Step 1.1

Combine the numerators over the common denominator.

$1 + \frac{4 - 6}{b} + \frac{\frac{4}{b^{2}}}{1} + \frac{- 16}{b^{2}}$

Step 1.2

Subtract $6$ from $4$ .

$1 + \frac{- 2}{b} + \frac{\frac{4}{b^{2}}}{1} + \frac{- 16}{b^{2}}$

Step 2

Simplify each term.

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Step 2.1

Move the negative in front of the fraction.

$1 - \frac{2}{b} + \frac{\frac{4}{b^{2}}}{1} + \frac{- 16}{b^{2}}$

Step 2.2

Divide $\frac{4}{b^{2}}$ by $1$ .

$1 - \frac{2}{b} + \frac{4}{b^{2}} + \frac{- 16}{b^{2}}$

Step 2.3

Move the negative in front of the fraction.

$1 - \frac{2}{b} + \frac{4}{b^{2}} - \frac{16}{b^{2}}$

Step 3

Combine fractions.

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Step 3.1

Combine the numerators over the common denominator.

$1 + \frac{- 2}{b} + \frac{4 - 16}{b^{2}}$

Step 3.2

Subtract $16$ from $4$ .

$1 + \frac{- 2}{b} + \frac{- 12}{b^{2}}$

Step 4

Simplify each term.

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Step 4.1

Move the negative in front of the fraction.

$1 - \frac{2}{b} + \frac{- 12}{b^{2}}$

Step 4.2

Move the negative in front of the fraction.

$1 - \frac{2}{b} - \frac{12}{b^{2}}$

Step 5

Combine into one fraction.

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Step 5.1

Write $1$ as a fraction with a common denominator.

$\frac{b}{b} - \frac{2}{b} - \frac{12}{b^{2}}$

Step 5.2

Combine the numerators over the common denominator.

$\frac{b - 2}{b} - \frac{12}{b^{2}}$

Step 6

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

$\frac{b - 2}{b} \cdot \frac{b}{b} - \frac{12}{b^{2}}$

Step 7

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

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Step 7.1

Multiply $\frac{b - 2}{b}$ by $\frac{b}{b}$ .

$\frac{(b - 2) b}{b \cdot b} - \frac{12}{b^{2}}$

Step 7.2

Multiply $b$ by $b$ .

$\frac{(b - 2) b}{b^{2}} - \frac{12}{b^{2}}$

Step 8

Combine the numerators over the common denominator.

$\frac{(b - 2) b - 12}{b^{2}}$

Step 9

Simplify the numerator.

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Step 9.1

Apply the distributive property.

$\frac{b \cdot b - 2 b - 12}{b^{2}}$

Step 9.2

Multiply $b$ by $b$ .

$\frac{b^{2} - 2 b - 12}{b^{2}}$