a cheap way to go about it is, use the LCD and multiply both sides by it.
now, notice the denominators, x, 4, 4x, clearly the LCD is 4x, so let's multiply both sides by that, to do away with the denominators,
[tex]\bf \cfrac{5}{x}+\cfrac{3}{4}=\cfrac{8}{4x}\implies \boxed{4x}\left( \cfrac{5}{x}+\cfrac{3}{4} \right)=\boxed{4x}\cdot \cfrac{8}{4x}\implies 20+3x=8
\\\\\\
3x=-12\implies x=\cfrac{-12}{3}\implies x=-4[/tex]
