Question

what is the solution of \\(\frac{5}{6x} = \frac{x}{6} + \frac{2x}{3}\\)?
a. 1 or -1
b. 5 or 3
c. 0 only
d. \\(\frac{5}{3}\\) only

Explanation:

Step1: Simplify right-hand side

$\frac{x}{6} + \frac{2x}{3} = \frac{x + 4x}{6} = \frac{5x}{6}$

Step2: Set equal to left-hand side

$\frac{5}{6x} = \frac{5x}{6}$

Step3: Cross-multiply to eliminate denominators

$5×6 = 5x×6x$ → $30 = 30x^2$

Step4: Solve for $x^2$

$x^2 = 1$ → $x = ±1$

Answer:

A. 1 or -1