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

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

Step 1

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

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

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

Combine.

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

Step 2

Apply the distributive property.

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

Step 3

Simplify by cancelling.

Cancel the common factor of $9 x$ .

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

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $3$ by $10$ .

$\frac{x \cdot 10 + 30}{9 x^{2} \frac{5}{3} + 9 x^{2} \frac{5}{x}}$

Cancel the common factor of $3$ .

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

$\frac{x \cdot 10 + 30}{3 (3 x^{2}) \frac{5}{3} + 9 x^{2} \frac{5}{x}}$

Cancel the common factor.

$\frac{x \cdot 10 + 30}{3 (3 x^{2}) \frac{5}{3} + 9 x^{2} \frac{5}{x}}$

Rewrite the expression.

$\frac{x \cdot 10 + 30}{3 x^{2} \cdot 5 + 9 x^{2} \frac{5}{x}}$

Multiply $5$ by $3$ .

$\frac{x \cdot 10 + 30}{15 x^{2} + 9 x^{2} \frac{5}{x}}$

Cancel the common factor of $x$ .

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

$\frac{x \cdot 10 + 30}{15 x^{2} + x (9 x) \frac{5}{x}}$

Cancel the common factor.

$\frac{x \cdot 10 + 30}{15 x^{2} + x (9 x) \frac{5}{x}}$

Rewrite the expression.

$\frac{x \cdot 10 + 30}{15 x^{2} + 9 x \cdot 5}$

Multiply $5$ by $9$ .

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

Step 4

Simplify terms.

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

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

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

Factor $10$ out of $30$ .

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

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

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

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

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

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

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

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

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

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

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

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

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $x + 3$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{2}{3 x}$

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

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