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

1. Jun 23, 2004

### 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.

2. Jun 23, 2004

### Muzza

You have that:

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

Then A - 1/A = what?

3. Jun 23, 2004

### trip7

Muzza:
Im sure this is easy but Im completely missing the logic. I havent done this kind of math in a while and hoping you could explain the logic.

4. Jun 23, 2004

### Gokul43201

Staff Emeritus
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.

5. Jun 23, 2004

### trip7

Thanks Gokul43201:

Ok, now I got it.