Tricky Algebra question - simplification, fractions and square roots

[RonnyDennis]

My dad just sent me this algebra question out of the blue. I can’t seem to find the right strategy to get me started let alone solve the question!

The question is...

If x=(√3)/2

Then prove that ((1+x)/(1+√(1+x)))+ ((1-x)/(1-√(1-x))) = 1

I hope my typing came through correctly, so I’ve attached a photo as well

 

[lev888]

I would simplify the expression on the left hand side, then plug in the x value to simplify further. Looks like a²-b² = (a+b)(a-b) might be useful.

 

[MarkFL]

I would utilize the fact that:

[MATH]2\pm\sqrt{3}=\frac{(\sqrt{3}\pm1)^2}{2}[/MATH]
This will allow for rapid simplification.

 

[Harry_the_cat]

Isn't your Dad great!!