Algebra Examples

$\frac{4}{5 x} - \frac{2 x}{5}$

Step 1

To write $- \frac{2 x}{5}$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$\frac{4}{5 x} - \frac{2 x}{5} \cdot \frac{x}{x}$

Step 2

Simplify terms.

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Step 2.1

Multiply $\frac{2 x}{5}$ by $\frac{x}{x}$ .

$\frac{4}{5 x} - \frac{2 x \cdot x}{5 x}$

Step 2.2

Combine the numerators over the common denominator.

$\frac{4 - 2 x \cdot x}{5 x}$

Step 3

Simplify the numerator.

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Step 3.1

Factor $2$ out of $4 - 2 x \cdot x$ .

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Step 3.1.1

Factor $2$ out of $4$ .

$\frac{2 (2) - 2 x \cdot x}{5 x}$

Step 3.1.2

Factor $2$ out of $- 2 x \cdot x$ .

$\frac{2 (2) + 2 (- x \cdot x)}{5 x}$

Step 3.1.3

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

$\frac{2 (2 - x \cdot x)}{5 x}$

Step 3.2

Multiply $x$ by $x$ by adding the exponents.

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Step 3.2.1

Move $x$ .

$\frac{2 (2 - (x \cdot x))}{5 x}$

Step 3.2.2

Multiply $x$ by $x$ .

$\frac{2 (2 - x^{2})}{5 x}$