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

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

Multiply the numerator and denominator of the complex fraction by $9 x$ .

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

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

Combine.

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

Apply the distributive property.

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

Simplify by cancelling.

Cancel the common factor of $9$ .

Factor $9$ out of $9 x$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $3 x$ .

Factor $3 x$ out of $9 x$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $9$ .

Factor $9$ out of $9 x$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $x$ by $x^{2}$ by adding the exponents.

Multiply $x$ by $x^{2}$ .

Raise $x$ to the power of $1$ .

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

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Add $1$ and $2$ .

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

Simplify the denominator.

Factor $x$ out of $x^{3} + 9 x \cdot - 1$ .

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

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

Factor $x$ out of $9 x \cdot - 1$ .

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

Factor $x$ out of $x \cdot x^{2} + x (9 \cdot - 1)$ .

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

Multiply $9$ by $- 1$ .

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

Rewrite $x^{2} - 9$ in a factored form.

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

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

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 3$ .

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

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

Cancel the common factor of $x + 3$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{1}{x (x - 3)}$

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

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