Please help w/ simplifying complex expressions

[Tilleigh 18]

Hi. Can someone please help me solve the following complex expressions??

1)

5-2x^-1
----------
5+2x^-1

2) 6x(x-1)^-1/2 - 5(x-1)^1/2

THANKS!

 

[Denis]

Hints: x^(-1) = 1/x and (x-1)^(-1/2) = 1 / (x-1)^(1/2)

CAUTION: that's bad: (x-1)^1/2 ; means ((x-1)^1) divided by 2
use BRACKETS: (x-1)^(1/2)

 

[Loren]

5-2x^-1
---------- = \(\displaystyle \frac{5-2(\frac{1}{x})}{5+2(\frac{1}{x})}\)
5+2x^-1

2) 6x(x-1)^(-1/2) - 5(x-1)^(1/2) =\(\displaystyle 6x \cdot \frac{1}{(x-1)^{1/2}}-5 \cdot (\frac{1}{(x-1)^{1/2}}\)

Is that what you mean?