#### Answer

a.) $\frac{8}{3}$
b.) 3

#### Work Step by Step

a.) $\frac{2}{\frac{2}{3}}$ - $\frac{\frac{2}{3}}{2}$
Rewrite the problem to multiply by switching the denominator by its reciprocal
$\frac{2}{1}$$\times$$\frac{3}{2}$ - $\frac{2}{3}$$\times$$\frac{1}{2}$
Simplify
3 - $\frac{1}{3}$
Least Common Denominator of 1 and 3 = 3
$\frac{9}{3}$ - $\frac{1}{3}$ = $\frac{8}{3}$
b.) $\frac{\frac{2}{5} + \frac{1}{2}}{\frac{1}{10} + \frac{3}{15}}$
Find the Least Common Denominator for both the numerator and denominator
Numerator's LCM of 5 and 2 = 10
Denominator's LCM of 10 and 15 = 30
$\frac{\frac{4}{10} + \frac{5}{10}}{\frac{3}{30} + \frac{6}{30}}$
Simplify
$\frac{\frac{9}{10}}{\frac{9}{30}}$
Multiply by denominator's reciprocal
$\frac{9}{10}$$\times$$\frac{30}{9}$ = $\frac{270}{90}$ = 3