Calculus Examples

$\frac{x}{x - \frac{1}{2}}$

Step 1

Simplify the denominator.

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Step 1.1

To write $x$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{x}{x \cdot \frac{2}{2} - \frac{1}{2}}$

Step 1.2

Combine $x$ and $\frac{2}{2}$ .

$\frac{x}{\frac{x \cdot 2}{2} - \frac{1}{2}}$

Step 1.3

Combine the numerators over the common denominator.

$\frac{x}{\frac{x \cdot 2 - 1}{2}}$

Step 1.4

Move $2$ to the left of $x$ .

$\frac{x}{\frac{2 x - 1}{2}}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$x \frac{2}{2 x - 1}$

Step 3

Combine $x$ and $\frac{2}{2 x - 1}$ .

$\frac{x \cdot 2}{2 x - 1}$

Step 4

Move $2$ to the left of $x$ .

$\frac{2 x}{2 x - 1}$