Question on Writing an Expression as a Single Quotient

[LynaEllrodt]

Question: (Sqrt (x+1)) - x times 1/ 2 (Sqrt (x+1)) / 1+x x> -1

Instructions: Write each expression as a single quotient in which only positive exponents and/or radicals appear.

I have only been able to reach (1+X)^(1/2) - x times 2(1+x)^(1/2) / 1+x

I am not sure if this is correct.

Thank you for the help!

Lyna

 

[stapel]

Question: (Sqrt (x+1)) - x times 1/ 2 (Sqrt (x+1)) / 1+x x> -1

Do "X" and "x" mean the same thing? (This is not standard mathematical practice, to please pardon me if they are meant to be different.)

Do you mean the following?

. . . . .\(\displaystyle \L \frac{\left({ \sqrt{x\,+\,1}\,-\,x }\right) \,\left({ \frac{1}{2}\,\sqrt{x\,+\,1} }\right)}{1\,+\,x}\,\,\mbox{for}\,x\,>\,-1\)

Please reply with confirmation or correction. Thank you.

Eliz.

 

[LynaEllrodt]

(Sqrt(1+x)) - x* 1/(2 sqrt(1 +x))
---------------------------------------------------------
1+ x
This is how the problem is written.
Thanks[/i]

 

[stapel]

(Sqrt(1+x)) - x* 1/(2 sqrt(1 +x))
---------------------------------------------------------
1+ x
This is how the problem is written.

So the expression is the following?

. . . . .\(\displaystyle \L \frac{\left({ \sqrt{x\,+\,1}\,-\,x }\right) \,\left({ \frac{1}{2\sqrt{x\,+\,1}} }\right)}{1\,+\,x}\,\,\mbox{for}\,x\,>\,-1\)

Please reply with confirmation or correction. Thank you.

Eliz.

 

[LynaEllrodt]

yes except for the 1st one.. It is Sqrt of 1+x..

 

[stapel]

yes except for the 1st one.. It is Sqrt of 1+x..

Since 1 + x = x + 1, there is no (mathematical) difference between the two. (Note: Grouping symbols are important: "sqrt 1 + x" means "sqrt[1] + x", not "sqrt[1 + x]".)

A good first step would be to multiply out the numerator, to get (1/2) - (x)/(2sqrt[x + 1]). Then rationalize the denominator of that second term.

Eliz.