Complex Fraction w/ Negative Exponent

[Tigertigre2000]

2(1-x)^(1/2) -x(1-x)^(-1/2) over x-1

How do you solve this... since you have the exponent as a negative.
How would you get rid of the exponent to solve it out. I just need the first steps then I'll be able to solve the rest of the problem.

Hopefully you can understand the equation since it's very long.
Well I'll be waiting your reply. Thanks I really I appriciate your time.

 

[stapel]

Treat the negative exponent in the usual way:

. . . . .\(\displaystyle \L 2\sqrt{1\,-\,x}\,-\,\frac{x}{\sqrt{1\,-\,x}}\)

Go for the common denominator:

. . . . .\(\displaystyle \L \frac{2(1\,-\,x)}{\sqrt{1\,-\,x}}\,-\,\frac{x}{\sqrt{1\,-\,x}}\)

Multiply out the parentheses in the first fraction, combine the numerators, and then see what you can do with the "x - 1" that I didn't include in the above.

Hope that helps.

Eliz.

 

[soroban]

Hello, Tigertigre2000!

It is not an equation . . . There's nothing to "solve".
We are expected to simplify it.

\(\displaystyle \L\frac{2(1\,-\,x)^{\frac{1}{2}}\:-\:x(1\,-\,x)^{-\frac{1}{2}}}{x\,-\,1}\)

Multiply top and bottom by \(\displaystyle (1\,-\,x)^{\frac{1}{2}}\)

\(\displaystyle \L\;\;\frac{(1\,-\,x)^{\frac{1}{2}}}{(1\,-\,x)^{\frac{1}{2}}}\,\cdot\,\frac{2(1\,-\,x)^{\frac{1}{2}}\,-\,x(1\,-\,x)^{-\frac{1}{2}}}{x\,-\,1} \;=\;\frac{2(1\,-\,x) \,- \,x}{(x\,-\,1)(1\,-\,x)^{\frac{1}{2}}}\)


\(\displaystyle \L\;\;=\;\frac{2\,-\,2x\,-\,x}{-(1\,-\,x)(1\,-\,x)^{\frac{1}{2}}} \;=\;\frac{2\,-\,3x}{-(1\,-\,x)^{\frac{3}{2}}} \;=\;\frac{3x\,-\,2}{(1\,-\,x)^{\frac{3}{2}}}\)

 

[Tigertigre2000]

Thanks

That really helps, no wonder I was getting so confused.
Thanks Soroban

P.S. Just a question, how do you put that table in with the eqaution. (See I'm kinda new to this posting , I would appriciate it if you could tell me).

 

[stapel]

Re: Thanks

how do you put that table in with the eqaution.

"Table"...? "Equation"...?

If you mean "how would I format the expression as Soroban did", please review the LaTeX links in the "Forum Help" pull-down menu at the very top of the page.

If you mean something else, please forgive my confusion and reply with clarification. Thank you.

Eliz.