Basic Math Examples

\frac{3 (2^{n}) - 4 \cdot 2^{n - 2}}{2^{n} - 2^{n - 1}}

$\frac{3 (2^{n}) - 4 \cdot 2^{n - 2}}{2^{n} - 2^{n - 1}}$

Step 1

Simplify the numerator.

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Step 1.1

Multiply

- 4 \cdot 2^{n - 2}

$- 4 \cdot 2^{n - 2}$ .

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Step 1.1.1

Factor out negative.

\frac{3 \cdot 2^{n} - (4 \cdot 2^{n - 2})}{2^{n} - 2^{n - 1}}

$\frac{3 \cdot 2^{n} - (4 \cdot 2^{n - 2})}{2^{n} - 2^{n - 1}}$

Step 1.1.2

Rewrite

4

$4$ as

2^{2}

$2^{2}$ .

\frac{3 \cdot 2^{n} - (2^{2} \cdot 2^{n - 2})}{2^{n} - 2^{n - 1}}

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

Step 1.1.3

Use the power rule

a^{m} a^{n} = a^{m + n}

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

\frac{3 \cdot 2^{n} - 2^{2 + n - 2}}{2^{n} - 2^{n - 1}}

$\frac{3 \cdot 2^{n} - 2^{2 + n - 2}}{2^{n} - 2^{n - 1}}$

Step 1.1.4

Subtract

2

$2$ from

2

$2$ .

\frac{3 \cdot 2^{n} - 2^{n + 0}}{2^{n} - 2^{n - 1}}

$\frac{3 \cdot 2^{n} - 2^{n + 0}}{2^{n} - 2^{n - 1}}$

Step 1.1.5

Add

n

$n$ and

0

$0$ .

\frac{3 \cdot 2^{n} - 2^{n}}{2^{n} - 2^{n - 1}}

$\frac{3 \cdot 2^{n} - 2^{n}}{2^{n} - 2^{n - 1}}$

\frac{3 \cdot 2^{n} - 2^{n}}{2^{n} - 2^{n - 1}}

$\frac{3 \cdot 2^{n} - 2^{n}}{2^{n} - 2^{n - 1}}$

Step 1.2

Subtract

2^{n}

$2^{n}$ from

3 \cdot 2^{n}

$3 \cdot 2^{n}$ .

\frac{2 \cdot 2^{n}}{2^{n} - 2^{n - 1}}

$\frac{2 \cdot 2^{n}}{2^{n} - 2^{n - 1}}$

\frac{2 \cdot 2^{n}}{2^{n} - 2^{n - 1}}

$\frac{2 \cdot 2^{n}}{2^{n} - 2^{n - 1}}$

Step 2

Multiply

2

$2$ by

2^{n}

$2^{n}$ .

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Step 2.1

Raise

2

$2$ to the power of

1

$1$ .

\frac{2^{1} \cdot 2^{n}}{2^{n} - 2^{n - 1}}

$\frac{2^{1} \cdot 2^{n}}{2^{n} - 2^{n - 1}}$

Step 2.2

Use the power rule

a^{m} a^{n} = a^{m + n}

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

\frac{2^{1 + n}}{2^{n} - 2^{n - 1}}

$\frac{2^{1 + n}}{2^{n} - 2^{n - 1}}$

\frac{2^{1 + n}}{2^{n} - 2^{n - 1}}

$\frac{2^{1 + n}}{2^{n} - 2^{n - 1}}$