#### Answer

a. Restriction values $: 0$
b. Solution set $:\{ 3 \}$

#### Work Step by Step

$\frac{5}{2x} - \frac{8}{9} = \frac{1}{18} - \frac{1}{3x}$
a. $x =0 $ makes the denominator zero. So, $x \ne 0.$
b. $\frac{5}{2x} - \frac{8}{9} = \frac{1}{18} - \frac{1}{3x};x \ne 0;$
Take LCD on both sides.
$\frac{45-16x}{18x} = \frac{x-6}{18x} ;x \ne 0;$
Multiply both sides by $18x$ to clear fraction part.
$18x(\frac{45-16x}{18x}) = 18x(\frac{x-6}{18x}) ;x \ne 0;$
$45-16x = x-6$
$45+6 = x+16x$
$51 = 17x$
$ x = \frac{51}{17}$
$x = 3$ is not part of the restriction values. So,
Solution set $:\{ 3 \}$