Multiple choice

Simplify the quadratic fraction: $\dfrac{-9+x^2}{x^2+2x-15}$

  1. $\dfrac{-x-3}{x+5}$
  2. $\dfrac{-x+3}{x+5}$
  3. $\dfrac{x+3}{x+5}$

  4. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Factor the numerator: x^2 - 9 = (x-3)(x+3). Factor the denominator: x^2 + 2x - 15 = (x+5)(x-3). The fraction is ((x-3)(x+3)) / ((x+5)(x-3)). Canceling (x-3) leaves (x+3)/(x+5).

AI explanation

Factor the numerator and the denominator to simplify the algebraic fraction. The numerator x^2 - 9 becomes (x - 3)(x + 3) using the difference of squares identity, and the denominator x^2 + 2x - 15 factors into (x + 5)(x - 3). Canceling the common (x - 3) term from both leaves (x + 3) / (x + 5).

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