Problem stating: if A = x - 1/x, find A - 1/A

[trip7]

I have a math problem stating:
if A = x - 1/x, find A - 1/A

I have no clue as to how to solve this. Any insight would be greatly appreciated.

 

[Muzza]

You have that:

A = x - 1/x
1/A = 1/(x - 1/x)

Then A - 1/A = what?

 

[trip7]

Muzza:
Im sure this is easy but I am completely missing the logic. I haven't done this kind of math in a while and hoping you could explain the logic.

 

[Gokul43201]

Just simplify the fractions...

A = x - \frac {1}{x} = \frac{x^2 - 1}{x}

So, ~ 1/A = \frac {x} {x^2 -1}

So, ~A - 1/A = \frac{x^2 - 1}{x} - \frac {x} {x^2 -1}

Take the lcm and simplify.

 

[trip7]

Thanks Gokul43201:

Ok, now I got it.