Question 736540
How do you solve
x^-1 - x^-2 = 3/4
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I think you have a typo.  Should that be x^-1 - x^-2 = (-)3/4 ???
Otherwise there are no real solutions, as you found.
To solve move -3/4 to the LHS of the equation and multiply through by x^2:
(3/4)x^2 + x - 1 = 0 -> x^2 + 4/3x - 4/3 = 0
We can cleverly factor this (knowing the answer ahead of time helps ;-)) as:
(x+2)(x-2/3) = 0
Now we can read off the answers x=-2, x=2/3