ratio question

 (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

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