In the posted problem, v = √.
Here is the problem with the intended notation:
If x>0, then 1 / [√(2x) + √x] =
A. 1 / √(3x)
B. 1/ 2√(2x)
c. 1 / x√2
D. (√2-1) / √x
E. (1+√2) / √x
Note the following:
(√x + √y)(√x - √y) = x-y.
Thus:
1 / [√(2x) + √x]
= 1 /
(√x)(√2+1)
= (1)
(√2-1) / (√x)(√2+1)
(√2-1)
=
(√2-1) / (√x)
(2-1)
= (√2-1) / √x
The correct answer is
D.
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