Basic Math Examples

$\frac{\sqrt{45}}{7} + \frac{2}{x}$

Step 1

Simplify the numerator.

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Step 1.1

Rewrite $45$ as $3^{2} \cdot 5$ .

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Step 1.1.1

Factor $9$ out of $45$ .

$\frac{\sqrt{9 (5)}}{7} + \frac{2}{x}$

Step 1.1.2

Rewrite $9$ as $3^{2}$ .

$\frac{\sqrt{3^{2} \cdot 5}}{7} + \frac{2}{x}$

Step 1.2

Pull terms out from under the radical.

$\frac{3 \sqrt{5}}{7} + \frac{2}{x}$

Step 2

To write $\frac{3 \sqrt{5}}{7}$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$\frac{3 \sqrt{5}}{7} \cdot \frac{x}{x} + \frac{2}{x}$

Step 3

To write $\frac{2}{x}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{3 \sqrt{5}}{7} \cdot \frac{x}{x} + \frac{2}{x} \cdot \frac{7}{7}$

Step 4

Write each expression with a common denominator of $7 x$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{3 \sqrt{5}}{7}$ by $\frac{x}{x}$ .

$\frac{3 \sqrt{5} x}{7 x} + \frac{2}{x} \cdot \frac{7}{7}$

Step 4.2

Multiply $\frac{2}{x}$ by $\frac{7}{7}$ .

$\frac{3 \sqrt{5} x}{7 x} + \frac{2 \cdot 7}{x \cdot 7}$

Step 4.3

Reorder the factors of $x \cdot 7$ .

$\frac{3 \sqrt{5} x}{7 x} + \frac{2 \cdot 7}{7 x}$

Step 5

Combine the numerators over the common denominator.

$\frac{3 \sqrt{5} x + 2 \cdot 7}{7 x}$

Step 6

Multiply $2$ by $7$ .

$\frac{3 \sqrt{5} x + 14}{7 x}$