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

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

Step 1

Multiply the numerator and denominator of the complex fraction by $x^{2}$ .

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

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

Combine.

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

Step 2

Apply the distributive property.

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

Step 3

Simplify by cancelling.

Cancel the common factor of $x^{2}$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $x$ .

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 4

Simplify the numerator.

Rewrite using the commutative property of multiplication.

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

Multiply $x^{2}$ by $x$ by adding the exponents.

Move $x$ .

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

Multiply $x$ by $x^{2}$ .

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

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

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

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

Add $1$ and $2$ .

$\frac{2 x^{3} + x^{2} \cdot 4}{2 + x}$

Move $4$ to the left of $x^{2}$ .

$\frac{2 x^{3} + 4 \cdot x^{2}}{2 + x}$

Factor $2 x^{2}$ out of $2 x^{3} + 4 x^{2}$ .

Factor $2 x^{2}$ out of $2 x^{3}$ .

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

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

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

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

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

Step 5

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

Reorder terms.

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

Cancel the common factor.

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

Divide $2 x^{2}$ by $1$ .

$2 x^{2}$

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

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