## Intermediate Algebra for College Students (7th Edition)

$\dfrac{x^2+9}{x^2-9}$
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, $\dfrac{\dfrac{3}{x}+\dfrac{x}{3}}{\dfrac{x}{3}-\dfrac{3}{x}}=\dfrac{x^2+9}{x^2-9}$