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

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

Multiply the numerator and denominator of the complex fraction by $6 x^{2}$ .

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

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

Combine.

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

Apply the distributive property.

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

Simplify by cancelling.

Cancel the common factor of $x$ .

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $2$ by $6$ .

$\frac{12 x + 6 x^{2} \frac{1}{3 x^{2}}}{6 x^{2} \cdot 1 + 6 x^{2} \frac{1}{6 x}}$

Cancel the common factor of $3 x^{2}$ .

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

$\frac{12 x + 3 x^{2} (2) \frac{1}{3 x^{2}}}{6 x^{2} \cdot 1 + 6 x^{2} \frac{1}{6 x}}$

Cancel the common factor.

$\frac{12 x + 3 x^{2} \cdot 2 \frac{1}{3 x^{2}}}{6 x^{2} \cdot 1 + 6 x^{2} \frac{1}{6 x}}$

Rewrite the expression.

$\frac{12 x + 2}{6 x^{2} \cdot 1 + 6 x^{2} \frac{1}{6 x}}$

Cancel the common factor of $6 x$ .

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

$\frac{12 x + 2}{6 x^{2} \cdot 1 + 6 x (x) \frac{1}{6 x}}$

Cancel the common factor.

$\frac{12 x + 2}{6 x^{2} \cdot 1 + 6 x \cdot x \frac{1}{6 x}}$

Rewrite the expression.

$\frac{12 x + 2}{6 x^{2} \cdot 1 + x}$

Factor $2$ out of $12 x + 2$ .

Factor $2$ out of $12 x$ .

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

Factor $2$ out of $2$ .

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

Factor $2$ out of $2 (6 x) + 2 (1)$ .

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

Simplify the denominator.

Factor $x$ out of $6 x^{2} \cdot 1 + x$ .

Factor $x$ out of $6 x^{2} \cdot 1$ .

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

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

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

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

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

Factor $x$ out of $x (6 x \cdot 1) + x \cdot 1$ .

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

Multiply $6$ by $1$ .

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

Cancel the common factor of $6 x + 1$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{2}{x}$

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

Related Questions

Support LCMGCF.com by disabling your adblocker.