Simplify (6+3x)/(2/(x^2)+1/x)

$\frac{6 + 3 x}{\frac{2}{x^{2}} + \frac{1}{x}}$

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

Multiply $\frac{6 + 3 x}{\frac{2}{x^{2}} + \frac{1}{x}}$ by $\frac{x^{2}}{x^{2}}$ .

$\frac{x^{2}}{x^{2}} \cdot \frac{6 + 3 x}{\frac{2}{x^{2}} + \frac{1}{x}}$

Combine.

$\frac{x^{2} (6 + 3 x)}{x^{2} (\frac{2}{x^{2}} + \frac{1}{x})}$

Apply the distributive property.

$\frac{x^{2} \cdot 6 + x^{2} (3 x)}{x^{2} \frac{2}{x^{2}} + x^{2} \frac{1}{x}}$

Simplify by cancelling.

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

Cancel the common factor.

$\frac{x^{2} \cdot 6 + x^{2} (3 x)}{x^{2} \frac{2}{x^{2}} + x^{2} \frac{1}{x}}$

Rewrite the expression.

$\frac{x^{2} \cdot 6 + x^{2} (3 x)}{2 + x^{2} \frac{1}{x}}$

Cancel the common factor of $x$ .

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

$\frac{x^{2} \cdot 6 + x^{2} (3 x)}{2 + x \cdot x \frac{1}{x}}$

Cancel the common factor.

$\frac{x^{2} \cdot 6 + x^{2} (3 x)}{2 + x \cdot x \frac{1}{x}}$

Rewrite the expression.

$\frac{x^{2} \cdot 6 + x^{2} (3 x)}{2 + x}$

Simplify the numerator.

Move $6$ to the left of $x^{2}$ .

$\frac{6 \cdot x^{2} + x^{2} (3 x)}{2 + x}$

Rewrite using the commutative property of multiplication.

$\frac{6 x^{2} + 3 x^{2} x}{2 + x}$

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

Move $x$ .

$\frac{6 x^{2} + 3 (x \cdot x^{2})}{2 + x}$

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

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

$\frac{6 x^{2} + 3 (x^{1} x^{2})}{2 + x}$

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

$\frac{6 x^{2} + 3 x^{1 + 2}}{2 + x}$

Add $1$ and $2$ .

$\frac{6 x^{2} + 3 x^{3}}{2 + x}$

Factor $3 x^{2}$ out of $6 x^{2} + 3 x^{3}$ .

Factor $3 x^{2}$ out of $6 x^{2}$ .

$\frac{3 x^{2} (2) + 3 x^{3}}{2 + x}$

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

$\frac{3 x^{2} (2) + 3 x^{2} (x)}{2 + x}$

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

$\frac{3 x^{2} (2 + x)}{2 + x}$

Cancel the common factor of $2 + x$ .

Cancel the common factor.

$\frac{3 x^{2} (2 + x)}{2 + x}$

Divide $3 x^{2}$ by $1$ .

$3 x^{2}$

Simplify (6+3x)/(2/(x^2)+1/x)

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