Basic Math Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

Factor $a$ out of $a b$ .

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

Step 1.3

Factor $a$ out of $a \cdot a + a (b)$ .

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

Step 2

Combine.

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

Step 3

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

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Step 3.1

Factor $a$ out of $a (a + b) (2 b)$ .

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

Step 3.2

Cancel the common factors.

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Step 3.2.1

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

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

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

Step 4

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

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Step 4.1

Factor $b$ out of $(a + b) (2 b)$ .

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

Step 4.2

Cancel the common factors.

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Step 4.2.1

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

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

Step 4.2.2

Cancel the common factor.

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

Step 4.2.3

Rewrite the expression.

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

Step 5

Move $2$ to the left of $a + b$ .

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