Question

\[(x + \frac{1}{x})^2 - \frac{3}{2}(x - \frac{1}{x}) = 4\]

Answer 1

expand it first
multiply both sides by a multiple of x to get rid of the denominator
move everything to one side
then attempt to factor

Answer 2

Finally you will get :

\[(x - \frac{1}{x})^2 - \frac{3}{2}(x - \frac{1}{x}) = 0\]

Answer 3

\[x - \frac{1}{x} = 0 \implies x^2 = 1\]

Answer 4

Or :

\[x - \frac{1}{x} = \frac{3}{2}\]

Answer 5

@waterineyes whered the 4 go?

Answer 6

\[(x + \frac{1}{x})^2 - 4 = (x - \frac{1}{x})^2\]

Answer 7

oh wait is a simple substitution
\[u=x+\frac{1}{x}\]
from there its a quadratic equation
solve for u then solve for x

Answer 8

Then what will you put for x - 1/x ??