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Solve the equation: x^2/((x-2)(x-3))=2/(x-2)+6/((x-2)(x-3))?
When you end up with 2 candidates for rootship; x=0, x=2, you find that 0 is a root since it satisfies the equation, like so...
However, 2 is not, division by 0 is not allowed.
Remember, checking is not merely a superfluos step but an essential part of the work.
1 Answer
- 1 decade agoFavorite Answer
x^2/((x-2)(x-3))=2/(x-2)+6/((x-2)(x-3))
multiply each term by the L.C.M i.e. (x-2)(x-3)
x^2/((x-2)(x-3)) * (x-2)(x-3) =2/(x-2) * (x-2)(x-3) +6/((x-2)(x-3)) * (x-2)(x-3)
The common factors cancel off, leaving
x^2 = 2*(x-3)+6
x^2 = 2x-6+6
x^2 - 2x = 0
Factorise x(x-2) = 0
x = 0
or
x-2 = 0
x=2 ( not acceptable because the terms become divisible by 0)
Ans. x=0
Source(s): school lessons
