Hey there, Guest!
So, let's go through this problem step-by-step:
First, let's format it like this: \(\frac{x+1/x}{x-2/x}=\frac{5}{4}\)
\(\frac{x^2+1}{x^2-2}=\frac{5}{4}\)
Step 1: Multiply both sides by \(x^2-2\).
\(x^2+1=\frac{5}{4}x^2+\frac{-5}{2}\)
\(x^2+1-\frac{5}{4}x^2=\frac{5}{4}x^2+\frac{-5}{2}-\frac{5}{4}x^2\) (Subtract \(5/4x^2\) from both sides.)
\(-\frac{1}{4}x^2+1=\frac{-5}{2}\)
\(-\frac{1}{4}x^2+1-1=-\frac{5}{2}-1\) (Subtract from both sides.)
\(\frac{-\frac{1}{4}x^2}{-1/4}=\frac{\frac{-7}{2}}{-1/4}\)
\(x^2=14\)
Therefore \(x=\sqrt{14}\) and \(-\sqrt{14}\).
Hope this helped! :)
( ゚д゚)つ Bye