Algebra Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

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

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

Step 1.3

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

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

Step 1.4

Factor $x$ out of $x \cdot x + x \cdot 1$ .

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

Step 2

To write $\frac{1}{x}$ as a fraction with a common denominator, multiply by $\frac{x + 1}{x + 1}$ .

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

Step 3

Multiply $\frac{1}{x}$ by $\frac{x + 1}{x + 1}$ .

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

Step 4

Combine the numerators over the common denominator.

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

Step 5

Subtract $2$ from $1$ .

$\frac{x - 1}{x (x + 1)}$