Simplify (1/x+1/(x^2))/(1/9+1/(3x))

$\frac{\frac{1}{x} + \frac{1}{x^{2}}}{\frac{1}{9} + \frac{1}{3 x}}$

Step 1

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

Multiply $\frac{\frac{1}{x} + \frac{1}{x^{2}}}{\frac{1}{9} + \frac{1}{3 x}}$ by $\frac{9 x^{2}}{9 x^{2}}$ .

$\frac{9 x^{2}}{9 x^{2}} \cdot \frac{\frac{1}{x} + \frac{1}{x^{2}}}{\frac{1}{9} + \frac{1}{3 x}}$

Combine.

$\frac{9 x^{2} (\frac{1}{x} + \frac{1}{x^{2}})}{9 x^{2} (\frac{1}{9} + \frac{1}{3 x})}$

Step 2

Apply the distributive property.

$\frac{9 x^{2} \frac{1}{x} + 9 x^{2} \frac{1}{x^{2}}}{9 x^{2} \frac{1}{9} + 9 x^{2} \frac{1}{3 x}}$

Step 3

Simplify by cancelling.

Cancel the common factor of $x$ .

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

$\frac{x (9 x) \frac{1}{x} + 9 x^{2} \frac{1}{x^{2}}}{9 x^{2} \frac{1}{9} + 9 x^{2} \frac{1}{3 x}}$

Cancel the common factor.

$\frac{x (9 x) \frac{1}{x} + 9 x^{2} \frac{1}{x^{2}}}{9 x^{2} \frac{1}{9} + 9 x^{2} \frac{1}{3 x}}$

Rewrite the expression.

$\frac{9 x + 9 x^{2} \frac{1}{x^{2}}}{9 x^{2} \frac{1}{9} + 9 x^{2} \frac{1}{3 x}}$

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

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

$\frac{9 x + x^{2} \cdot 9 \frac{1}{x^{2}}}{9 x^{2} \frac{1}{9} + 9 x^{2} \frac{1}{3 x}}$

Cancel the common factor.

$\frac{9 x + x^{2} \cdot 9 \frac{1}{x^{2}}}{9 x^{2} \frac{1}{9} + 9 x^{2} \frac{1}{3 x}}$

Rewrite the expression.

$\frac{9 x + 9}{9 x^{2} \frac{1}{9} + 9 x^{2} \frac{1}{3 x}}$

Cancel the common factor of $9$ .

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

$\frac{9 x + 9}{9 (x^{2}) \frac{1}{9} + 9 x^{2} \frac{1}{3 x}}$

Cancel the common factor.

$\frac{9 x + 9}{9 x^{2} \frac{1}{9} + 9 x^{2} \frac{1}{3 x}}$

Rewrite the expression.

$\frac{9 x + 9}{x^{2} + 9 x^{2} \frac{1}{3 x}}$

Cancel the common factor of $3 x$ .

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

$\frac{9 x + 9}{x^{2} + 3 x (3 x) \frac{1}{3 x}}$

Cancel the common factor.

$\frac{9 x + 9}{x^{2} + 3 x (3 x) \frac{1}{3 x}}$

Rewrite the expression.

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

Step 4

Simplify with factoring out.

Factor $9$ out of $9 x + 9$ .

Factor $9$ out of $9 x$ .

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

Factor $9$ out of $9$ .

$\frac{9 (x) + 9 (1)}{x^{2} + 3 x}$

Factor $9$ out of $9 (x) + 9 (1)$ .

$\frac{9 (x + 1)}{x^{2} + 3 x}$

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

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

$\frac{9 (x + 1)}{x \cdot x + 3 x}$

Factor $x$ out of $3 x$ .

$\frac{9 (x + 1)}{x \cdot x + x \cdot 3}$

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

$\frac{9 (x + 1)}{x (x + 3)}$

Simplify (1/x+1/(x^2))/(1/9+1/(3x))

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