## Intermediate Algebra (6th Edition)

$x=\{2,10\}$
Multiplying both sides by the $LCD= 4x ,$ then the given equation, $\dfrac{x}{4}+\dfrac{5}{x}=3 ,$ simplifies to \begin{array}{l}\require{cancel} x(x)+4(5)=4x(3) \\\\ x^2+20=12x \\\\ x^2-12x+20=0 \\\\ (x-10)(x-2)=0 \\\\ x=\{2,10\} .\end{array} Upon checking, both solutions satisfy the original equation. Hence, there is $x=\{2,10\} .$