Basic Math Examples

$\frac{\frac{a + b}{a b}}{\frac{a^{2} b^{2}}{4 a^{3} b}}$

Step 1

Cancel the common factor of $a^{2}$ and $a^{3}$ .

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Step 1.1

Factor $a^{2}$ out of $a^{2} b^{2}$ .

$\frac{\frac{a + b}{a b}}{\frac{a^{2} (b^{2})}{4 a^{3} b}}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $a^{2}$ out of $4 a^{3} b$ .

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

Step 1.2.2

Cancel the common factor.

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

Step 1.2.3

Rewrite the expression.

$\frac{\frac{a + b}{a b}}{\frac{b^{2}}{4 a b}}$

Step 2

Cancel the common factor of $b^{2}$ and $b$ .

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Step 2.1

Factor $b$ out of $b^{2}$ .

$\frac{\frac{a + b}{a b}}{\frac{b \cdot b}{4 a b}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $b$ out of $4 a b$ .

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

Step 2.2.2

Cancel the common factor.

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

Step 2.2.3

Rewrite the expression.

$\frac{\frac{a + b}{a b}}{\frac{b}{4 a}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$\frac{a + b}{a b} \cdot \frac{4 a}{b}$

Step 4

Cancel the common factor of $a$ .

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Step 4.1

Factor $a$ out of $a b$ .

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

Step 4.2

Factor $a$ out of $4 a$ .

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

Step 4.3

Cancel the common factor.

$\frac{a + b}{a b} \cdot \frac{a \cdot 4}{b}$

Step 4.4

Rewrite the expression.

$\frac{a + b}{b} \cdot \frac{4}{b}$

Step 5

Multiply $\frac{a + b}{b}$ by $\frac{4}{b}$ .

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

Step 6

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

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

Step 7

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

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

Step 8

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

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

Step 9

Add $1$ and $1$ .

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

Step 10

Move $4$ to the left of $a + b$ .

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