Algebra Examples

$\frac{4 a b}{c x + d x} \times \frac{a x + b x}{2 a b}$

Step 1

Factor $x$ out of $c x + d x$ .

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Step 1.1

Factor $x$ out of $c x$ .

$\frac{4 a b}{x c + d x} \cdot \frac{a x + b x}{2 a b}$

Step 1.2

Factor $x$ out of $d x$ .

$\frac{4 a b}{x c + x d} \cdot \frac{a x + b x}{2 a b}$

Step 1.3

Factor $x$ out of $x c + x d$ .

$\frac{4 a b}{x (c + d)} \cdot \frac{a x + b x}{2 a b}$

Step 2

Factor $x$ out of $a x + b x$ .

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Step 2.1

Factor $x$ out of $a x$ .

$\frac{4 a b}{x (c + d)} \cdot \frac{x a + b x}{2 a b}$

Step 2.2

Factor $x$ out of $b x$ .

$\frac{4 a b}{x (c + d)} \cdot \frac{x a + x b}{2 a b}$

Step 2.3

Factor $x$ out of $x a + x b$ .

$\frac{4 a b}{x (c + d)} \cdot \frac{x (a + b)}{2 a b}$

Step 3

Cancel the common factor of $2 a b$ .

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Step 3.1

Factor $2 a b$ out of $4 a b$ .

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

Step 3.2

Cancel the common factor.

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

Step 3.3

Rewrite the expression.

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

Step 4

Cancel the common factor of $x$ .

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Step 4.1

Cancel the common factor.

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

Step 4.2

Rewrite the expression.

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

Step 5

Multiply $\frac{2}{c + d}$ by $a + b$ .

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