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Clavis TMUA Set B Paper 2 · Q13

Paper 2Logic & proofAlgebra

Consider the following attempt to solve the equation (x−3)(x+1)=2(x−3)(x-3)(x+1)=2(x-3).

  • (I) Dividing both sides by (x−3)(x-3) gives x+1=2x+1=2.
  • (II) Therefore x=1x=1.
  • (III) So the only solution is x=1x=1.

Which one of the following is true?

AThe working is correct.
BThe working is incorrect: x=1x=1 is not a solution of the original equation, and the error arises as a result of step (I).
CThe working is incorrect: there is a further solution of the original equation, and the error arises as a result of step (I).
DThe working is incorrect: there is a further solution of the original equation, and the error arises as a result of step (II).
EThe working is incorrect: there is a further solution of the original equation, but every step shown is valid.
FThe working is incorrect: the original equation has no solutions.

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