Chapter 1 - Section 1.3 - Algebraic Expressions - 1.3 Exercises - Page 34: 95

$(x^{2}+1)^{1/2}+2(x^{2}+1)^{-1/2}=\dfrac{x^{2}+3}{\sqrt{x^{2}+1}}$

$(x^{2}+1)^{1/2}+2(x^{2}+1)^{-1/2}$ Take out common afctor $(x^{2}+1)^{-1/2}$: $(x^{2}+1)^{1/2}+2(x^{2}+1)^{-1/2}=(x^{2}+1)^{-1/2}[(x^{2}+1)+2]=...$ $...=(x^{2}+1)^{-1/2}(x^{2}+3)=\dfrac{x^{2}+3}{\sqrt{x^{2}+1}}$