2021 · Q82
What should be added to 1/[(x−2)(x−4)], to get (2x−5)/[(x²−5x+6)(x−4)]?
Elementary MathematicsAlgebra
- A1/(x² − 7x + 12)
- B1/(x² + 7x + 12)
- C1/(x² − 7x − 12)
- D1/(x² + 7x − 12)
Explanation
The required addition is the difference (2x−5)/[(x−2)(x−3)(x−4)] − 1/[(x−2)(x−4)]. Combining over the common denominator gives [(2x−5) − (x−3)]/[(x−2)(x−3)(x−4)] = (x−2)/[(x−2)(x−3)(x−4)]. Cancelling (x−2) leaves 1/[(x−3)(x−4)] = 1/(x²−7x+12). Hence option A.