2021 · Q22
If A + B = (x² − 8)/(x + 2) and A − B = (−x² + 2x + 4)/(x + 2), then what is B equal to ?
Elementary MathematicsAlgebra
- A(x² − 4)/(x² + 4x + 4)
- B(x² − 4)/(x² − 4x + 4)
- C(2x² − 7x + 3)/(2x − 1)
- D(2x² + 7x − 3)/(2x − 1)
Explanation
Subtracting: (A+B) − (A−B) = 2B = (x² − 8 + x² − 2x − 4)/(x+2) = (2x² − 2x − 12)/(x+2). Factoring the numerator, 2x² − 2x − 12 = 2(x − 3)(x + 2), so B = (x − 3)(x+2)/(x+2) = x − 3. Writing x − 3 with denominator (2x − 1) gives (2x² − 7x + 3)/(2x − 1). This is option (c).