Simplify (4+2/x)/(x/4+1/8)

$\frac{4 + \frac{2}{x}}{\frac{x}{4} + \frac{1}{8}}$

Step 1

Multiply the numerator and denominator of the complex fraction by $x \cdot 8$ .

Multiply $\frac{4 + \frac{2}{x}}{\frac{x}{4} + \frac{1}{8}}$ by $\frac{x \cdot 8}{x \cdot 8}$ .

$\frac{x \cdot 8}{x \cdot 8} \cdot \frac{4 + \frac{2}{x}}{\frac{x}{4} + \frac{1}{8}}$

Combine.

$\frac{x \cdot 8 (4 + \frac{2}{x})}{x \cdot 8 (\frac{x}{4} + \frac{1}{8})}$

Step 2

Apply the distributive property.

$\frac{x \cdot 8 \cdot 4 + x \cdot 8 \frac{2}{x}}{x \cdot 8 \frac{x}{4} + x \cdot 8 \frac{1}{8}}$

Step 3

Simplify by cancelling.

Cancel the common factor of $x$ .

Factor $x$ out of $x \cdot 8$ .

$\frac{x \cdot 8 \cdot 4 + x (8) \frac{2}{x}}{x \cdot 8 \frac{x}{4} + x \cdot 8 \frac{1}{8}}$

Cancel the common factor.

$\frac{x \cdot 8 \cdot 4 + x \cdot 8 \frac{2}{x}}{x \cdot 8 \frac{x}{4} + x \cdot 8 \frac{1}{8}}$

Rewrite the expression.

$\frac{x \cdot 8 \cdot 4 + 8 \cdot 2}{x \cdot 8 \frac{x}{4} + x \cdot 8 \frac{1}{8}}$

Multiply $8$ by $2$ .

$\frac{x \cdot 8 \cdot 4 + 16}{x \cdot 8 \frac{x}{4} + x \cdot 8 \frac{1}{8}}$

Cancel the common factor of $4$ .

Factor $4$ out of $x \cdot 8$ .

$\frac{x \cdot 8 \cdot 4 + 16}{4 (x \cdot 2) \frac{x}{4} + x \cdot 8 \frac{1}{8}}$

Cancel the common factor.

$\frac{x \cdot 8 \cdot 4 + 16}{4 (x \cdot 2) \frac{x}{4} + x \cdot 8 \frac{1}{8}}$

Rewrite the expression.

$\frac{x \cdot 8 \cdot 4 + 16}{x \cdot 2 x + x \cdot 8 \frac{1}{8}}$

Raise $x$ to the power of $1$ .

$\frac{x \cdot 8 \cdot 4 + 16}{2 (x^{1} x) + x \cdot 8 \frac{1}{8}}$

Raise $x$ to the power of $1$ .

$\frac{x \cdot 8 \cdot 4 + 16}{2 (x^{1} x^{1}) + x \cdot 8 \frac{1}{8}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{x \cdot 8 \cdot 4 + 16}{2 x^{1 + 1} + x \cdot 8 \frac{1}{8}}$

Add $1$ and $1$ .

$\frac{x \cdot 8 \cdot 4 + 16}{2 x^{2} + x \cdot 8 \frac{1}{8}}$

Cancel the common factor of $8$ .

Factor $8$ out of $x \cdot 8$ .

$\frac{x \cdot 8 \cdot 4 + 16}{2 x^{2} + 8 \cdot x \frac{1}{8}}$

Cancel the common factor.

$\frac{x \cdot 8 \cdot 4 + 16}{2 x^{2} + 8 \cdot x \frac{1}{8}}$

Rewrite the expression.

$\frac{x \cdot 8 \cdot 4 + 16}{2 x^{2} + x}$

Step 4

Simplify the numerator.

Move $8$ to the left of $x$ .

$\frac{8 \cdot x \cdot 4 + 16}{2 x^{2} + x}$

Multiply $4$ by $8$ .

$\frac{32 x + 16}{2 x^{2} + x}$

Factor $16$ out of $32 x + 16$ .

Factor $16$ out of $32 x$ .

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

Factor $16$ out of $16$ .

$\frac{16 (2 x) + 16 (1)}{2 x^{2} + x}$

Factor $16$ out of $16 (2 x) + 16 (1)$ .

$\frac{16 (2 x + 1)}{2 x^{2} + x}$

Step 5

Simplify terms.

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

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

$\frac{16 (2 x + 1)}{x (2 x) + x}$

Raise $x$ to the power of $1$ .

$\frac{16 (2 x + 1)}{x (2 x) + x^{1}}$

Factor $x$ out of $x^{1}$ .

$\frac{16 (2 x + 1)}{x (2 x) + x \cdot 1}$

Factor $x$ out of $x (2 x) + x \cdot 1$ .

$\frac{16 (2 x + 1)}{x (2 x + 1)}$

Cancel the common factor of $2 x + 1$ .

Cancel the common factor.

$\frac{16 (2 x + 1)}{x (2 x + 1)}$

Rewrite the expression.

$\frac{16}{x}$

Simplify (4+2/x)/(x/4+1/8)

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