Answer
a. $0$
b. $\{ \frac{1}{4} \}$
Work Step by Step
$\frac{7}{2x} - \frac{5}{3x} = \frac{22}{3}$
a. $x=0$, makes the denominator zero, so it is the restricted value.
b. $\frac{7}{2x} - \frac{5}{3x} = \frac{22}{3} ; x \ne 0;$
Multiply both sides, by the LCD $6x$.
$6x(\frac{7}{2x} - \frac{5}{3x}) = 6x(\frac{22}{3}) ; x \ne 0;$
Using Distributive property,
$6x(\frac{7}{2x}) - 6x( \frac{5}{3x}) = 6x(\frac{22}{3}) ; x \ne 0;$
Divide out common factors.
$3(7) -2(5) = 2x(22)$
$21-10 = 44x$
$11 = 44x$
$x = \frac{11}{44}$
$x = \frac{1}{4}$
$\frac{1}{4} $ is not the restricted value. Solution Set : $\{\frac{1}{4} \}$
