Solve the Rational Equation: x(x²-9)/(x²+3x) = 0

To solve this problem, we need to find the values of $x$ that make the equation $\frac{x(x^2-9)}{x^2+3x}=0$ true. The steps are as follows:

• Step 1: Simplify the Numerator
  The numerator is $x(x^2 - 9)$. Recognize $x^2 - 9$ as a difference of squares, which can be factored to $(x-3)(x+3)$. Thus, the numerator becomes $x(x-3)(x+3)$.

• Step 2: Simplify the Denominator
  The denominator is $x^2 + 3x$, which can be factored as $x(x + 3)$.

• Step 3: Rewrite the Equation
  Now, the equation is rewritten as:
  $\frac{x(x-3)(x+3)}{x(x+3)} = 0$

• Step 4: Cancel Common Factors
  Assuming $x \neq 0$ (since division by zero is undefined), cancel $x$ and $(x+3)$:
  $\frac{x-3}{1} = 0$

• Step 5: Solve for $x$
  The reduced equation $x - 3 = 0$ gives the solution $x = 3$.

• Step 6: Check for Restrictions
  We previously canceled $x$ and $x+3$, so $x \neq 0$ and $x \neq -3$ must be considered as part of the domain.

Therefore, the solution to the problem is $x = 3$.

This corresponds to choice 2 in the given multiple-choice options.