Simplify (4ab)/(cx+dx)*(ax+bx)/(2ab)

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

Step 1

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

Factor $x$ out of $c x$ .

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

Factor $x$ out of $d x$ .

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

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 $a x + b x$ .

Factor $x$ out of $a x$ .

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

Factor $x$ out of $b x$ .

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

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 $2 a b$ .

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 4

Cancel the common factor of $x$ .

Cancel the common factor.

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

Rewrite the expression.

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

Step 5

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

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