1. Problem (a): Rationalize and simplify the expression $$\frac{\sqrt{10}}{\sqrt{5} - 2}$$. 2. To rationalize the denominator, multiply numerator and denominator by the conjugate of the denominator: $$\sqrt{5} + 2$$. 3. Multiply: $$\frac{\sqrt{10}}{\sqrt{5} - 2} \times \frac{\sqrt{5} + 2}{\sqrt{5} + 2} = \frac{\sqrt{10}(\sqrt{5} + 2)}{(\sqrt{5} - 2)(\sqrt{5} + 2)}$$. 4. Simplify the denominator using difference of squares: $$(\sqrt{5})^2 - 2^2 = 5 - 4 = 1$$. 5. Simplify the numerator: $$\sqrt{10} \times \sqrt{5} + \sqrt{10} \times 2 = \sqrt{50} + 2\sqrt{10} = 5\sqrt{2} + 2\sqrt{10}$$. 6. Final simplified expression for (a): $$5\sqrt{2} + 2\sqrt{10}$$. 7. Problem (b): Simplify the expression $$\frac{\sqrt{4 + h} - 2}{h}$$. 8. Multiply numerator and denominator by the conjugate of the numerator: $$\sqrt{4 + h} + 2$$. 9. Multiply: $$\frac{\sqrt{4 + h} - 2}{h} \times \frac{\sqrt{4 + h} + 2}{\sqrt{4 + h} + 2} = \frac{(\sqrt{4 + h})^2 - 2^2}{h(\sqrt{4 + h} + 2)} = \frac{4 + h - 4}{h(\sqrt{4 + h} + 2)}$$. 10. Simplify numerator: $$\frac{h}{h(\sqrt{4 + h} + 2)}$$. 11. Cancel $h$: $$\frac{1}{\sqrt{4 + h} + 2}$$. 12. Final simplified expression for (b): $$\frac{1}{\sqrt{4 + h} + 2}$$. These steps show how to rationalize denominators and simplify expressions involving radicals.