2016 · Q34
If 4x + 3a = 0, then what is the value of x²+ax+a²/x³-a³ - x²-ax+a²/x³+a³ ?
Elementary MathematicsAlgebra
- A-4/7a
- B7/a
- C-32/7a
- D24/7a
Explanation
From 4x+3a = 0 we get x = −3a/4. Note (x²+ax+a²)/(x³−a³) = 1/(x−a) and (x²−ax+a²)/(x³+a³) = 1/(x+a). Their difference is 2a/(x²−a²) = 2a/(9a²/16−a²) = 2a/(−7a²/16) = −32/(7a) (option C).