Solve the following equation:

$\dfrac{x}{3} + \dfrac{9}{x} = 4$

Given, $\dfrac{x}{3} + \dfrac{9}{x} = 4$.

Taking L.C.M. we get,

$\Rightarrow \dfrac{x^2 + 27}{3x} = 4$

By cross multiplication we get,

⇒ x² + 27 = 12x

⇒ x² - 12x + 27 = 0

⇒ x² - 9x - 3x + 27 = 0

⇒ x(x - 9) - 3(x - 9) = 0

⇒ (x - 9)(x - 3) = 0

⇒ x - 9 = 0 or x - 3 = 0

⇒ x = 9 or x = 3.

Hence, roots of the given equations are 3, 9.