How Do You Simplify Complex Algebraic Expressions?

[beaf123]

Homework Statement

I have the expression [((1-x)/x) * x^(2/1-x)] / x^(2x/1-x)

I want to simplify this expression.

Homework Equations

None

The Attempt at a Solution

I am not so good with algebra. But I tried to find a common factor for x^(2/1-x)] / (x^2x)/1-x and then add them. However, it got really ugly so I think I did something wrong. Anyone knows how to simplify this one?[/B]

 

[Dick]

Homework Statement

I have the expression [((1-x)/x) * x^(2/1-x)] / x^(2x/1-x)

I want to simplify this expression.

Homework Equations

None

The Attempt at a Solution

I am not so good with algebra. But I tried to find a common factor for x^(2/1-x)] / (x^2x)/1-x and then add them. However, it got really ugly so I think I did something wrong. Anyone knows how to simplify this one?[/B]

x^a/x^b=x^(a-b). In your case a=2/(1-x) and b=2x/(1-x). Concentrate on simplifying a-b. BTW notice I wrote 2/(1-x) instead of 2/1-x which would be interpreted as (2/1)-x. That's not what I think you mean. Always fully parenthesize expressions!

 

[beaf123]

Thanks a lot.

Very smootely my answer becomes x(1-x)