Chapter R - Section R.8 - nth Roots; Rational Exponents - R.8 Assess Your Understanding - Page 80: 109

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

We simplify the equation as follows: $3x^{-\frac{1}{2}}+\frac{3}{2}x^{\frac{1}{2}}$ $=\frac{3}{x^{\frac{1}{2}}}+\frac{3x^{\frac{1}{2}}}{2}$ $=\frac{6}{2x^{\frac{1}{2}}}+\frac{3x}{2x^{\frac{1}{2}}}$ $=\frac{6+3x}{2x^{\frac{1}{2}}}$ $=\frac{3(2+x)}{2x^{\frac{1}{2}}}$