Question 563798
{{{(sqrt(x^2+1)sqrt(x^2+1))/sqrt(x^2+1) + 8/sqrt(x^2+1) = sqrt(x^2+9)}}}

---
square 
{{{(x^2+9)/(x^2+1) = x^2+9}}}
--
multiply by denominator
{{{x^4+18x^2+81 = (x^2+9)(x^2+1)}}}
__
{{{x^4+18x^2+81 = x^4+10x^2+9}}}
---
set equal to zero
{{{8x^2+72 = 0}}}
--
{{{8x^2 = -72}}}
{{{x^2 = -9}}}
{{{x = 3i}}} or {{{x= -3i}}}