SOLUTION: Hi - In a recent demonstration, somebody went from this (square root of (1 + x-squared))/x to this square root of (1 + 1/x-squared) They're both obviously eq

Question 107071: Hi - In a recent demonstration, somebody went from this

(square root of (1 + x-squared))/x
to this

square root of (1 + 1/x-squared)

They're both obviously equivalent, as both result in the same answer for values of x. Can you help me to understand how this manipulation was performed, and how these two forms relate? Thanks!

Answer by HyperBrain(694) (Show Source): You can put this solution on YOUR website!

THIS IS INTERESTING!!! Thanks! I love this type of problem.
Note that the equation above is the same as

By cross multiplication,

If you square both sides,

-------------we're getting close! watch the next move or
maybe you can do it. hint:it IS easy
The final move....
--------------can you guess what I did? From , I
just interchanged and

Therefore, is proven to be true.

Power up,
HyperBrain!
RELATED QUESTIONS
Need to simplify: the square root of (x-3)squared + (y-5)squared = square root of... (answered by edjones)

x - 1/x = square root of 6, then x squared + 1/x squared =? (answered by mananth)

simplify square root of x squared minus 2x plus 1 (answered by jim_thompson5910)

The diameter of a circle has endpoints P (0; 0) and Q(8;-4) : The equation of the circle... (answered by Alan3354)

Hi again. I found another problem that is confusing. square root of 2x = the square root (answered by stanbon)

square root of x squared... (answered by haileytucki)

I need to solve x2(this is x squared)+2x-4=0 I tried to solve by adding 4 to both sides... (answered by ewatrrr)

1 squared + the square root of 3... (answered by tutorcecilia)

x=1+the square root of x squared + x + 2x times the square root of x - the square root of (answered by AnlytcPhil)