Digital SAT Math Practice Question #1186

⚡ Hack the Test: Numerical Substitution or Graphing **1. Numerical Substitution (Quickest for multiple choice):** Choose a simple value for \( x \) that does not make the original denominator zero (e.g., \( x=1 \)). Calculate \( E(1) \): \( E(1) = \frac{1^3-1^2-6(1)}{1^3-9(1)} = \frac{1-1-6}{1-9} = \frac{-6}{-8} = \frac{3}{4} \) Now, substitute \( x=1 \) into each option: * Option A: \( \frac{1+2}{1+3} = \frac{3}{4} \) (Matches! This is likely the answer.) * Option B: \( \frac{1-2}{1+3} = \frac{-1}{4} \) (Does not match) * Option C: \( \frac{1+2}{1-3} = \frac{3}{-2} \) (Does not match) * Option D: \( \frac{1}{1+3} = \frac{1}{4} \) (Does not match) Since only Option A matches, it must be the correct answer. **2. Graphing (Using Desmos or a graphing calculator):** Graph the original function: \( y = \frac{x^3-x^2-6x}{x^3-9x} \) Then, graph each option one by one: * Graph \( y = \frac{x+2}{x+3} \) If the graph of this option perfectly overlaps the graph of the original function (except for the holes at \( x=0 \) and \( x=3 \)), then it is the equivalent expression. This method visually confirms the equivalence and is very reliable for 'equivalent expression' questions.