Appendix A - Review - A.7 nth Roots; Rational Exponents - A.7 Assess Your Understanding - Page A61: 77

$ \frac{x(3x^2+2)}{(x^2+1)^{1/2}}$

$2x(x^2+1)^{1/2}+x^2\cdot\frac{1}{2}(x^2+1)^{-1/2}\cdot2x=2x(x^2+1)^{1/2}+\frac{x^3}{(x^2+1)^{1/2}}=\frac{2x(x^2+1)+x^3}{(x^2+1)^{1/2}}=\frac{3x^3+2x}{(x^2+1)^{1/2}}=\frac{x(3x^2+2)}{(x^2+1)^{1/2}}$