Answer
a. $0$
b. $\{ 2 \}$
Work Step by Step
$\frac{2}{3x} + \frac{1}{4} = \frac{11}{6x} - \frac{1}{3}$
a. $x=0$, makes the denominator zero, it is the restricted value.
b. $\frac{2}{3x} + \frac{1}{4} = \frac{11}{6x} - \frac{1}{3} ; x \ne 0;$
Multiply both sides, by the LCD $12x$.
$12x(\frac{2}{3x} + \frac{1}{4}) = 12x(\frac{11}{6x} - \frac{1}{3}) ; x \ne 0;$
Using Distributive property,
$12x(\frac{2}{3x}) + 12x(\frac{1}{4}) = 12x(\frac{11}{6x}) - 12x(\frac{1}{3}) ; x \ne 0;$
Divide out common factors.
$8 + 3x = 22 - 4x$
$3x + 4x = 22 - 8$
$7x = 14$
$x = 2$
$2 $ is not the restricted value, Solution : $\{ 2 \}$
