a)
\sqrt{2\frac{7}{9}}-\sqrt{\frac{5}{9}}=\sqrt{\frac{25}{9}}-\sqrt{\frac{5}{9}}=\frac{\sqrt{25}}{\sqrt9}-\frac{\sqrt5}{\sqrt9}=\frac{5}{3}-\frac{\sqrt5}{3}=\frac{5-\sqrt5}{3}
b)
\sqrt{\frac{18}{25}}-\sqrt{\frac{32}{225}}=\frac{\sqrt{18}}{\sqrt{25}}-\frac{\sqrt{32}}{\sqrt{225}}=\frac{\sqrt{9*2}}{5}-\frac{\sqrt{16*2}}{15}=\frac{3\sqrt2}{5}-\frac{4\sqrt2}{15}=
=\frac{3*3\sqrt2}{15}-\frac{4\sqrt2}{15}=\frac{9\sqrt2-4\sqrt2}{15}=\frac{\not5^1\sqrt2}{\not15^3}=\frac{\sqrt2}{3}