Pre-Algebra Examples

$\frac{5}{x^{2}} + \frac{6}{5 x}$

Step 1

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

$\frac{5}{x^{2}} \cdot \frac{5}{5} + \frac{6}{5 x}$

Step 2

To write $\frac{6}{5 x}$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$\frac{5}{x^{2}} \cdot \frac{5}{5} + \frac{6}{5 x} \cdot \frac{x}{x}$

Step 3

Write each expression with a common denominator of $5 x^{2}$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

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

$\frac{5 \cdot 5}{x^{2} \cdot 5} + \frac{6}{5 x} \cdot \frac{x}{x}$

Step 3.2

Multiply $\frac{6}{5 x}$ by $\frac{x}{x}$ .

$\frac{5 \cdot 5}{x^{2} \cdot 5} + \frac{6 x}{5 x \cdot x}$

Step 3.3

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

$\frac{5 \cdot 5}{x^{2} \cdot 5} + \frac{6 x}{5 (x^{1} x)}$

Step 3.4

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

$\frac{5 \cdot 5}{x^{2} \cdot 5} + \frac{6 x}{5 (x^{1} x^{1})}$

Step 3.5

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{5 \cdot 5}{x^{2} \cdot 5} + \frac{6 x}{5 x^{1 + 1}}$

Step 3.6

Add $1$ and $1$ .

$\frac{5 \cdot 5}{x^{2} \cdot 5} + \frac{6 x}{5 x^{2}}$

Step 3.7

Reorder the factors of $x^{2} \cdot 5$ .

$\frac{5 \cdot 5}{5 x^{2}} + \frac{6 x}{5 x^{2}}$

Step 4

Combine the numerators over the common denominator.

$\frac{5 \cdot 5 + 6 x}{5 x^{2}}$

Step 5

Multiply $5$ by $5$ .

$\frac{25 + 6 x}{5 x^{2}}$