Question: To solve the rational equation $\frac{2}{x} + \frac{3-x}{6} = \frac{5}{x+2}$, how can the expression $\frac{5}{x+2}$ be rewritten using the least common denominator?
1. **State the problem:** We want to rewrite the expression $$\frac{5}{x+2}$$ using the least common denominator (LCD) of all terms in the equation $$\frac{2}{x} + \frac{3-x}{6} = \frac{5}{x+2}$$.
2. **Identify denominators:** The denominators are $$x$$, $$6$$, and $$x+2$$.
3. **Find the least common denominator (LCD):** The LCD must include all factors:
$$\text{LCD} = 6x(x+2)$$
4. **Rewrite $$\frac{5}{x+2}$$ with the LCD:** Multiply numerator and denominator by the missing factors $$6x$$:
$$\frac{5}{x+2} = \frac{5 \times 6x}{(x+2) \times 6x} = \frac{30x}{6x(x+2)}$$
5. **Final rewritten expression:**
$$\frac{5}{x+2} = \frac{30x}{6x(x+2)}$$
This allows all terms in the equation to have the same denominator $$6x(x+2)$$ for easier solving.