Answer
a. Restricted Value : $0$
b. Solution Set : $\{ \frac{5}{12} \}$
Work Step by Step
$\frac{5}{x} = \frac{10}{3x} + 4$
a. It $x=0$, it makes the denominator zero, therefore, $x=0 $ is the restricted value.
b. $\frac{5}{x} = \frac{10}{3x} + 4 ; x \ne 0;$
Take LCD at the right hand side.
$\frac{5}{x} = \frac{10+12x}{3x} ; x \ne 0;$
Multiply both sides by $3x$ to clear fractional part.
$3x(\frac{5}{x}) = 3x(\frac{10+12x}{3x}) ; x \ne 0;$
$15 = 10+12x$
$15-10=12x$
$12x = 5$
$x= \frac{5}{12}$
$\frac{5}{12} $ is not the restricted value. Solution Set : $\{ \frac{5}{12} \}$
