Simplify ((x+8)/18)÷((2x^2+16x)/(16x))

$\frac{x + 8}{18} \div \frac{2 x^{2} + 16 x}{16 x}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{x + 8}{18} \cdot \frac{16 x}{2 x^{2} + 16 x}$

Step 2

Simplify terms.

Cancel the common factor of $2$ .

Factor $2$ out of $18$ .

$\frac{x + 8}{2 (9)} \cdot \frac{16 x}{2 x^{2} + 16 x}$

Factor $2$ out of $16 x$ .

$\frac{x + 8}{2 (9)} \cdot \frac{2 (8 x)}{2 x^{2} + 16 x}$

Cancel the common factor.

$\frac{x + 8}{2 \cdot 9} \cdot \frac{2 (8 x)}{2 x^{2} + 16 x}$

Rewrite the expression.

$\frac{x + 8}{9} \cdot \frac{8 x}{2 x^{2} + 16 x}$

Multiply $\frac{x + 8}{9}$ by $\frac{8 x}{2 x^{2} + 16 x}$ .

$\frac{(x + 8) (8 x)}{9 (2 x^{2} + 16 x)}$

Step 3

Simplify the denominator.

Factor $2 x$ out of $2 x^{2} + 16 x$ .

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

$\frac{(x + 8) \cdot 8 x}{9 (2 x (x) + 16 x)}$

Factor $2 x$ out of $16 x$ .

$\frac{(x + 8) \cdot 8 x}{9 (2 x (x) + 2 x (8))}$

Factor $2 x$ out of $2 x (x) + 2 x (8)$ .

$\frac{(x + 8) \cdot 8 x}{9 (2 x (x + 8))}$

$\frac{(x + 8) \cdot 8 x}{9 \cdot 2 x (x + 8)}$

Multiply $9$ by $2$ .

$\frac{(x + 8) \cdot 8 x}{18 x (x + 8)}$

Step 4

Reduce the expression by cancelling the common factors.

Cancel the common factor of $x + 8$ .

Cancel the common factor.

$\frac{(x + 8) \cdot 8 x}{18 x (x + 8)}$

Rewrite the expression.

$\frac{8 x}{18 x}$

Cancel the common factor of $8$ and $18$ .

Factor $2$ out of $8 x$ .

$\frac{2 (4 x)}{18 x}$

Cancel the common factors.

Factor $2$ out of $18 x$ .

$\frac{2 (4 x)}{2 (9 x)}$

Cancel the common factor.

$\frac{2 (4 x)}{2 (9 x)}$

Rewrite the expression.

$\frac{4 x}{9 x}$

Cancel the common factor of $x$ .

Cancel the common factor.

$\frac{4 x}{9 x}$

Rewrite the expression.

$\frac{4}{9}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{4}{9}$

Decimal Form:

$0.\overline{4}$

Simplify ((x+8)/18)÷((2x^2+16x)/(16x))

Related Questions

Support LCMGCF.com by disabling your adblocker.