Simplify the rational expression (x^2 - 9)/(x^2 - 3x).

• A. (x - 3)/x
• B. (x + 3)/x
• C. (x + 3)/(x - 3)
• D. x/(x - 3)

Answer: (B)

When simplifying a rational expression, factoring and canceling common factors is the key move. Factor the numerator as a difference of squares: x^2 - 9 = (x - 3)(x + 3). Factor the denominator: x^2 - 3x = x(x - 3). Cancel the common factor (x - 3) from top and bottom, leaving (x + 3)/x. Remember the original expression is undefined when x = 0 or x = 3, so the simplified form is valid for all x except 0 and 3. This matches the expression with numerator x + 3 over denominator x.