rationalize the denominator and simplify: \n\\frac{3\\sqrt{b}}{\\sqrt{b + 2}}

Explanation:

Step1: Multiply numerator and denominator by $\sqrt{b}$

$$\frac{3\sqrt{b}}{b}\times\frac{\sqrt{b}}{\sqrt{b}}=\frac{3b}{b\sqrt{b}}$$

Step2: Simplify the fraction

Cancel out the common factor $b$ in the numerator and denominator: $$\frac{3b}{b\sqrt{b}}=\frac{3}{\sqrt{b}}$$

Step3: Rationalize the denominator

Multiply numerator and denominator by $\sqrt{b}$: $$\frac{3}{\sqrt{b}}\times\frac{\sqrt{b}}{\sqrt{b}}=\frac{3\sqrt{b}}{b}$$

Answer:

$\frac{3\sqrt{b}}{b}$