Lcd Equation Bd6164

1. **State the problem:** We need to find the least common denominator (LCD) for the equation $$\frac{3}{x} - \frac{2}{x+2} = \frac{6}{2x+4}$$. 2. **Identify denominators:** The denominators are $$x$$, $$x+2$$, and $$2x+4$$. 3. **Factor denominators if possible:** Note that $$2x+4 = 2(x+2)$$. 4. **Find the LCD:** The LCD must include each factor the greatest number of times it appears in any denominator. - From $$x$$, we have factor $$x$$. - From $$x+2$$, we have factor $$x+2$$. - From $$2(x+2)$$, we have factor $$2$$ and $$x+2$$. 5. **Combine factors:** The LCD is $$2 \times x \times (x+2)$$ or $$2x(x+2)$$. 6. **Answer:** The least common denominator is $$2x(x+2)$$. This corresponds to the choice "2x(x+2)".