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

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

Step 1

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

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

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

Combine.

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

Step 2

Apply the distributive property.

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

Step 3

Simplify by cancelling.

Cancel the common factor of $3 x$ .

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $6 x^{2}$ .

Move the leading negative in $- \frac{1}{6 x^{2}}$ into the numerator.

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $2 x$ .

Move the leading negative in $- \frac{1}{2 x}$ into the numerator.

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

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $- 1$ by $3$ .

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

Step 4

Simplify the denominator.

Factor $3 x$ out of $6 x^{2} \cdot 1 - 3 x$ .

Factor $3 x$ out of $6 x^{2} \cdot 1$ .

$\frac{2 x - 1}{3 x (2 x \cdot 1) - 3 x}$

Factor $3 x$ out of $- 3 x$ .

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

Factor $3 x$ out of $3 x (2 x \cdot 1) + 3 x (- 1)$ .

$\frac{2 x - 1}{3 x (2 x \cdot 1 - 1)}$

Multiply $2$ by $1$ .

$\frac{2 x - 1}{3 x (2 x - 1)}$

Step 5

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

Cancel the common factor.

$\frac{2 x - 1}{3 x (2 x - 1)}$

Rewrite the expression.

$\frac{1}{3 x}$

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

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