Pre-Algebra Examples

$\frac{1}{x} + \frac{2}{x - 5}$

Step 1

To write $\frac{1}{x}$ as a fraction with a common denominator, multiply by $\frac{x - 5}{x - 5}$ .

$\frac{1}{x} \cdot \frac{x - 5}{x - 5} + \frac{2}{x - 5}$

Step 2

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

$\frac{1}{x} \cdot \frac{x - 5}{x - 5} + \frac{2}{x - 5} \cdot \frac{x}{x}$

Step 3

Write each expression with a common denominator of $x (x - 5)$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{1}{x}$ by $\frac{x - 5}{x - 5}$ .

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

Step 3.2

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

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

Step 3.3

Reorder the factors of $(x - 5) x$ .

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

Step 4

Combine the numerators over the common denominator.

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

Step 5

Add $x$ and $2 x$ .

$\frac{3 x - 5}{x (x - 5)}$