Answer
a. $0$
b. $\{ -2 \}$
Work Step by Step
$\frac{2}{x} + 3 = \frac{5}{2x} + \frac{13}{4}$
a. If $x=0$, it makes the denominator zero, therefore, $x=0 $ is the restricted value.
b. $\frac{2}{x} + 3 = \frac{5}{2x} + \frac{13}{4}; x \ne 0$
Multiply both sides, by $4x$, $4x$ is the LCD.
$4x(\frac{2}{x} + 3) = 4x(\frac{5}{2x} + \frac{13}{4}); x \ne 0$
$4x(\frac{2}{x}) +4x( 3) = 4x(\frac{5}{2x}) + 4x(\frac{13}{4}); x \ne 0$
$8+12x = 10 + 13x$
$8-10 = 13x - 12x$
$ x = -2$
$-2 $ is not the restricted value. Solution Set : $\{-2 \}$
