Question

Simplify \( \frac{(1+x)^{\frac{1}{2}}-2 x(1+x)^{-\frac{1}{2}}}{(1+x)^{\frac{1}{2}}} \)

Answer 1

\(\frac{(1+x)^{1/2}-2x(1+x){-1/2}}{(1+x)^{1/2}}\)

 = \(\frac{(1+x)^{-1/2}((1+x)-2x)}{(1+x)^{1/2}}\)

 = \(\frac{1-x}{(1+x)^{1/2+1/2}}\) = \(\frac{1-x}{1+x}\)