Finite Math Examples

$\frac{a + b}{\frac{a b}{\frac{a^{2} - b^{2}}{2 a^{3} b}}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

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

Step 2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = a$ and $b = b$ .

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

Step 3

Multiply the numerator by the reciprocal of the denominator.

$(a + b) (\frac{(a + b) (a - b)}{2 a^{3} b} \cdot \frac{1}{a b})$

Step 4

Combine fractions.

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Step 4.1

Combine.

$(a + b) \frac{(a + b) (a - b) \cdot 1}{2 a^{3} b (a b)}$

Step 4.2

Multiply $a + b$ by $1$ .

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

Step 5

Simplify the denominator.

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Step 5.1

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

$(a + b) \frac{(a + b) (a - b)}{2 (a^{1} a^{3}) b \cdot b}$

Step 5.2

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

$(a + b) \frac{(a + b) (a - b)}{2 a^{1 + 3} b \cdot b}$

Step 5.3

Add $1$ and $3$ .

$(a + b) \frac{(a + b) (a - b)}{2 a^{4} b \cdot b}$

Step 5.4

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

$(a + b) \frac{(a + b) (a - b)}{2 a^{4} (b^{1} b)}$

Step 5.5

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

$(a + b) \frac{(a + b) (a - b)}{2 a^{4} (b^{1} b^{1})}$

Step 5.6

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

$(a + b) \frac{(a + b) (a - b)}{2 a^{4} b^{1 + 1}}$

Step 5.7

Add $1$ and $1$ .

$(a + b) \frac{(a + b) (a - b)}{2 a^{4} b^{2}}$

Step 6

Multiply $a + b$ by $\frac{(a + b) (a - b)}{2 a^{4} b^{2}}$ .

$\frac{(a + b) ((a + b) (a - b))}{2 a^{4} b^{2}}$

Step 7

Simplify the numerator.

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Step 7.1

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

$\frac{{(a + b)}^{1} (a + b) (a - b)}{2 a^{4} b^{2}}$

Step 7.2

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

$\frac{{(a + b)}^{1} {(a + b)}^{1} (a - b)}{2 a^{4} b^{2}}$

Step 7.3

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

$\frac{{(a + b)}^{1 + 1} (a - b)}{2 a^{4} b^{2}}$

Step 7.4

Add $1$ and $1$ .

$\frac{{(a + b)}^{2} (a - b)}{2 a^{4} b^{2}}$