Chapter R - Section R.8 - nth Roots; Rational Exponents - R.8 Assess Your Understanding - Page 79: 87

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

We simplify: $\displaystyle \frac{x}{(1+x)^{1/2}}+2(1+x)^{1/2}=\frac{x}{(1+x)^{1/2}}+2(1+x)^{1/2}\frac{(1+x)^{1/2}}{(1+x)^{1/2}}=\frac{x+2(1+x)^{1/2}(1+x)^{1/2}}{(1+x)^{1/2}}=\frac{x+2(1+x)}{(1+x)^{1/2}}=\frac{x+2+2x}{(1+x)^{1/2}}=\frac{3x+2}{(1+x)^{1/2}}$