+129847 (x + 1/x):(x - 2/x) = 5:4
x + 1/x = (x^2 +1) / x (1)
x - 2/x = (x^2 - 2) / x (2)
Diviiding (1) by (2) we have
x^2 + 1 5
______ = ___ cross-multiply
x^2 - 2 4
4x^2 + 4 = 5x^2 - 10 rearrange as
x^2 - 14 = 0
x^2 = 14 take both roots
x = sqrt 14 x = -sqrt 14
+373 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
