Appendix A - Review - A.7 nth Roots; Rational Exponents - A.7 Assess Your Understanding - Page A61: 81

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

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