Simplify ( square root of 45)/7+2/x

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

Step 1

Simplify the numerator.

Rewrite

$45$ as

$3^{2} \cdot 5$ .

Factor

$9$ out of

$45$ .

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

Rewrite

$9$ as

$3^{2}$ .

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

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

$1$ .

Multiply

$\frac{3 \sqrt{5}}{7}$ by

$\frac{x}{x}$ .

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

Multiply

$\frac{2}{x}$ by

$\frac{7}{7}$ .

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

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

$7$ .

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

Simplify ( square root of 45)/7+2/x

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