Simplify (4x^2+36)/(4x)*1/(5x)

$\frac{4 x^{2} + 36}{4 x} \cdot \frac{1}{5 x}$

Step 1

Factor $4$ out of $4 x^{2} + 36$ .

Factor $4$ out of $4 x^{2}$ .

$\frac{4 (x^{2}) + 36}{4 x} \cdot \frac{1}{5 x}$

Factor $4$ out of $36$ .

$\frac{4 x^{2} + 4 \cdot 9}{4 x} \cdot \frac{1}{5 x}$

Factor $4$ out of $4 x^{2} + 4 \cdot 9$ .

$\frac{4 (x^{2} + 9)}{4 x} \cdot \frac{1}{5 x}$

Step 2

Combine.

$\frac{4 (x^{2} + 9) \cdot 1}{4 x (5 x)}$

Step 3

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$\frac{4 (x^{2} + 9) \cdot 1}{4 (x \cdot x) \cdot 5}$

Multiply $x$ by $x$ .

$\frac{4 (x^{2} + 9) \cdot 1}{4 x^{2} \cdot 5}$

Step 4

Multiply $4 (x^{2} + 9)$ by $1$ .

$\frac{4 (x^{2} + 9)}{4 x^{2} \cdot 5}$

Step 5

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 (x^{2} + 9)}{4 x^{2} \cdot 5}$

Rewrite the expression.

$\frac{x^{2} + 9}{x^{2} \cdot 5}$

Step 6

Move $5$ to the left of $x^{2}$ .

$\frac{x^{2} + 9}{5 x^{2}}$