SOLUTION: How do you solve x^-1 - x^-2 = 3/4 I tried the u substitution but did not get the correct answer. I keep getting -1/2 plus or minus i radical 2 over two But the answer I nee

Question 736540: How do you solve
x^-1 - x^-2 = 3/4
I tried the u substitution but did not get the correct answer. I keep getting -1/2 plus or minus i radical 2 over two
But the answer I need to get to is -2,2/3
Please help!
Found 2 solutions by josgarithmetic, htmentor:
Answer by josgarithmetic(39629) (Show Source): You can put this solution on YOUR website!
EDIT(small arithmetic mistake correction):
Realize your equation is the same as . LCD is , so multiply left and right members by . You should obtain this:

.

If you have that within your solution steps, you were doing well up to such point.

Simplifies further to ,
factorable into ---No. NOT factorable.
Use formula for solution to a quadratic equation. It will simplify to
or

The expected -2 or 2/3 is incorrect.

Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
How do you solve
x^-1 - x^-2 = 3/4
----------------------
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
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