Question

. In this section, you learned to simplify the complex fraction $\frac{{\displaystyle \frac{3}{x+2}}}{{\displaystyle \frac{x}{x^2-4}}}$

two ways: rewriting it as a division problem multiplying the numerator and denominator by the LCD Which method do you prefer? Why?

Short answer

Simplified expression

$\frac{3x-6}{x}$

Step-by-step solution

Step 1. Given information

$\frac{{\displaystyle \frac{3}{x+2}}}{{\displaystyle \frac{x}{x^2-4}}}$

Step 2. By LCD method

The LCD of the given expression is :$(x-2)(x+2)$

Multiplying numerator and denominator with LCD

$$\begin{gathered} \frac{{\displaystyle \frac{3}{x+2}(x-2)(x+2)}}{{\displaystyle \frac{x}{x^2-4}(x-2)(x+2)}} \\ \frac{3(x-2)}{x} \\ \frac{3x-6}{x} \end{gathered}$$

Step 3. By Division method

$$\begin{gathered} \frac{{\displaystyle \frac{3}{x+2}}}{{\displaystyle \frac{x}{x^2-4}}} \\ \frac{3}{x+2}\times \frac{x^2-4}{x} \\ \frac{3(x-2)}{x} \\ \frac{3x-6}{x} \end{gathered}$$

Step 4. Conclusion

I will prefer LCD method