Basic Math Examples

$\frac{4^{n + 1} - 4^{n - 1}}{4^{n}}$

Step 1

Split the fraction $\frac{4^{n + 1} - 4^{n - 1}}{4^{n}}$ into two fractions.

$\frac{4^{n + 1}}{4^{n}} + \frac{- 4^{n - 1}}{4^{n}}$

Step 2

Cancel the common factor of $4^{n + 1}$ and $4^{n}$ .

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Step 2.1

Factor $4^{n}$ out of $4^{n + 1}$ .

$\frac{4^{n} \cdot 4}{4^{n}} + \frac{- 4^{n - 1}}{4^{n}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Multiply by $1$ .

$\frac{4^{n} \cdot 4}{4^{n} \cdot 1} + \frac{- 4^{n - 1}}{4^{n}}$

Step 2.2.2

Cancel the common factor.

$\frac{4^{n} \cdot 4}{4^{n} \cdot 1} + \frac{- 4^{n - 1}}{4^{n}}$

Step 2.2.3

Rewrite the expression.

$\frac{4}{1} + \frac{- 4^{n - 1}}{4^{n}}$

Step 2.2.4

Divide $4$ by $1$ .

$4 + \frac{- 4^{n - 1}}{4^{n}}$

Step 3

Cancel the common factor of $4^{n - 1}$ and $4^{n}$ .

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Step 3.1

Factor $4^{n}$ out of $- 4^{n - 1}$ .

$4 + \frac{4^{n} (- 4^{- 1})}{4^{n}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Multiply by $1$ .

$4 + \frac{4^{n} (- 4^{- 1})}{4^{n} \cdot 1}$

Step 3.2.2

Cancel the common factor.

$4 + \frac{4^{n} (- 4^{- 1})}{4^{n} \cdot 1}$

Step 3.2.3

Rewrite the expression.

$4 + \frac{- 4^{- 1}}{1}$

Step 3.2.4

Divide $- 4^{- 1}$ by $1$ .

$4 - 4^{- 1}$

Step 4

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$4 - \frac{1}{4}$

Step 5

To write $4$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$4 \cdot \frac{4}{4} - \frac{1}{4}$

Step 6

Combine $4$ and $\frac{4}{4}$ .

$\frac{4 \cdot 4}{4} - \frac{1}{4}$

Step 7

Combine the numerators over the common denominator.

$\frac{4 \cdot 4 - 1}{4}$

Step 8

Simplify the numerator.

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Step 8.1

Multiply $4$ by $4$ .

$\frac{16 - 1}{4}$

Step 8.2

Subtract $1$ from $16$ .

$\frac{15}{4}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$\frac{15}{4}$

Decimal Form:

$3.75$

Mixed Number Form:

$3 \frac{3}{4}$