Question 246683
{{{x/4+4/x=17/4}}} get a common denominator on the left side
{{{x^2/4x + 16/4x = 17/4}}} collect terms
{{{(x^2 +16)/4x = 17/4}}} multiply both sides by 4x
{{{x^2 + 16 = 17x}}} move everything to one side and solve
{{{x^2 -17x + 16 = 0}}} we will just factor this one
{{{(x-16)(x-1) = 0}}}
So x is either 16 or 1. Both work, verify your answers