Simplify (5/3+5/x)/(10/(9x)+10/(3x^2))

$\frac{\frac{5}{3} + \frac{5}{x}}{\frac{10}{9 x} + \frac{10}{3 x^{2}}}$

Multiply the numerator and denominator of the complex fraction by $9 x^{2}$ .

Multiply $\frac{\frac{5}{3} + \frac{5}{x}}{\frac{10}{9 x} + \frac{10}{3 x^{2}}}$ by $\frac{9 x^{2}}{9 x^{2}}$ .

$\frac{9 x^{2}}{9 x^{2}} \cdot \frac{\frac{5}{3} + \frac{5}{x}}{\frac{10}{9 x} + \frac{10}{3 x^{2}}}$

Combine.

$\frac{9 x^{2} (\frac{5}{3} + \frac{5}{x})}{9 x^{2} (\frac{10}{9 x} + \frac{10}{3 x^{2}})}$

Apply the distributive property.

$\frac{9 x^{2} \frac{5}{3} + 9 x^{2} \frac{5}{x}}{9 x^{2} \frac{10}{9 x} + 9 x^{2} \frac{10}{3 x^{2}}}$

Simplify by cancelling.

Cancel the common factor of $3$ .

Factor $3$ out of $9 x^{2}$ .

$\frac{3 (3 x^{2}) \frac{5}{3} + 9 x^{2} \frac{5}{x}}{9 x^{2} \frac{10}{9 x} + 9 x^{2} \frac{10}{3 x^{2}}}$

Cancel the common factor.

$\frac{3 (3 x^{2}) \frac{5}{3} + 9 x^{2} \frac{5}{x}}{9 x^{2} \frac{10}{9 x} + 9 x^{2} \frac{10}{3 x^{2}}}$

Rewrite the expression.

$\frac{3 x^{2} \cdot 5 + 9 x^{2} \frac{5}{x}}{9 x^{2} \frac{10}{9 x} + 9 x^{2} \frac{10}{3 x^{2}}}$

Multiply $5$ by $3$ .

$\frac{15 x^{2} + 9 x^{2} \frac{5}{x}}{9 x^{2} \frac{10}{9 x} + 9 x^{2} \frac{10}{3 x^{2}}}$

Cancel the common factor of $x$ .

Factor $x$ out of $9 x^{2}$ .

$\frac{15 x^{2} + x (9 x) \frac{5}{x}}{9 x^{2} \frac{10}{9 x} + 9 x^{2} \frac{10}{3 x^{2}}}$

Cancel the common factor.

$\frac{15 x^{2} + x (9 x) \frac{5}{x}}{9 x^{2} \frac{10}{9 x} + 9 x^{2} \frac{10}{3 x^{2}}}$

Rewrite the expression.

$\frac{15 x^{2} + 9 x \cdot 5}{9 x^{2} \frac{10}{9 x} + 9 x^{2} \frac{10}{3 x^{2}}}$

Multiply $5$ by $9$ .

$\frac{15 x^{2} + 45 x}{9 x^{2} \frac{10}{9 x} + 9 x^{2} \frac{10}{3 x^{2}}}$

Cancel the common factor of $9 x$ .

Factor $9 x$ out of $9 x^{2}$ .

$\frac{15 x^{2} + 45 x}{9 x (x) \frac{10}{9 x} + 9 x^{2} \frac{10}{3 x^{2}}}$

Cancel the common factor.

$\frac{15 x^{2} + 45 x}{9 x \cdot x \frac{10}{9 x} + 9 x^{2} \frac{10}{3 x^{2}}}$

Rewrite the expression.

$\frac{15 x^{2} + 45 x}{x \cdot 10 + 9 x^{2} \frac{10}{3 x^{2}}}$

Cancel the common factor of $3 x^{2}$ .

Factor $3 x^{2}$ out of $9 x^{2}$ .

$\frac{15 x^{2} + 45 x}{x \cdot 10 + 3 x^{2} (3) \frac{10}{3 x^{2}}}$

Cancel the common factor.

$\frac{15 x^{2} + 45 x}{x \cdot 10 + 3 x^{2} \cdot 3 \frac{10}{3 x^{2}}}$

Rewrite the expression.

$\frac{15 x^{2} + 45 x}{x \cdot 10 + 3 \cdot 10}$

Multiply $3$ by $10$ .

$\frac{15 x^{2} + 45 x}{x \cdot 10 + 30}$

Simplify terms.

Factor $15 x$ out of $15 x^{2} + 45 x$ .

Factor $15 x$ out of $15 x^{2}$ .

$\frac{15 x (x) + 45 x}{x \cdot 10 + 30}$

Factor $15 x$ out of $45 x$ .

$\frac{15 x (x) + 15 x (3)}{x \cdot 10 + 30}$

Factor $15 x$ out of $15 x (x) + 15 x (3)$ .

$\frac{15 x (x + 3)}{x \cdot 10 + 30}$

Factor $10$ out of $x \cdot 10 + 30$ .

Factor $10$ out of $x \cdot 10$ .

$\frac{15 x (x + 3)}{10 \cdot x + 30}$

Factor $10$ out of $30$ .

$\frac{15 x (x + 3)}{10 \cdot x + 10 \cdot 3}$

Factor $10$ out of $10 \cdot x + 10 \cdot 3$ .

$\frac{15 x (x + 3)}{10 (x + 3)}$

Cancel the common factor of $15$ and $10$ .

Factor $5$ out of $15 x (x + 3)$ .

$\frac{5 (3 x (x + 3))}{10 (x + 3)}$

Cancel the common factors.

Factor $5$ out of $10 (x + 3)$ .

$\frac{5 (3 x (x + 3))}{5 (2 (x + 3))}$

Cancel the common factor.

$\frac{5 (3 x (x + 3))}{5 (2 (x + 3))}$

Rewrite the expression.

$\frac{3 x (x + 3)}{2 (x + 3)}$

Cancel the common factor of $x + 3$ .

Cancel the common factor.

$\frac{3 x (x + 3)}{2 (x + 3)}$

Rewrite the expression.

$\frac{3 x}{2}$

Simplify (5/3+5/x)/(10/(9x)+10/(3x^2))

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