Find the value of $\frac{1+2x}{1+\sqrt{1+2x}}+\frac{1-2x}{1-\sqrt{1-2x}}$ for $x=\frac{\sqrt3}{4}$.
Solution 1:
HINT...it may help you to use the fact that $$(1+\sqrt{3})^2=4+2\sqrt{3}$$ So $$\sqrt{1+\frac{\sqrt{3}}{2}}=?$$
Similarly with the $-$ sign