Problem
Match the given equation with the correct first step for solving it. \[ \frac{2 x+3}{x}+\frac{3}{x+3}=7 \] Choose the correct answer below. A. Let $u=(x+3)^{\frac{1}{3}}$ and $u^{2}=(x+3)^{\frac{2}{3}}$ B. Raise each side of the equation to the power $\frac{2}{3}$. C. Square each side of the equation. D. Cube each side of the equation. E. Multiply each side of the equation by $x(x+3)$.
Solution
Step 1 ：The given equation contains fractions. To eliminate the fractions, we can multiply each side of the equation by the least common multiple (LCM) of the denominators. In this case, the LCM of \(x\) and \(x+3\) is \(x(x+3)\). Therefore, the correct first step for solving the equation is to multiply each side of the equation by \(x(x+3)\). This corresponds to option E.
Step 2 ：Final Answer: \(\boxed{\text{E}}\)
