Answer
$\dfrac{x^2+9}{x^2-9}$
Work Step by Step
Given: $\dfrac{\dfrac{3}{x}+\dfrac{x}{3}}{\dfrac{x}{3}-\dfrac{3}{x}}$
Let us consider the numerator expression
$\dfrac{3}{x}+\dfrac{x}{3}=\dfrac{9+x^2}{3x}$ ...(1)
Now, we will consider the denominator expression.
$\dfrac{x}{3}-\dfrac{3}{x}=\dfrac{x^2-9}{3x}$ ...(2)
Divide equation (1) by (2).
Hence, $\dfrac{\dfrac{3}{x}+\dfrac{x}{3}}{\dfrac{x}{3}-\dfrac{3}{x}}=\dfrac{x^2+9}{x^2-9}$
