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Question
Solve the following quadratic equations by factorization:
`1/(x-2)+2/(x-1)=6/x` , x ≠ 0
Solution
We have been given
`1/(x-2)+2/(x-1)=6/x`
x2 - x + 2x2 - 4x = 6(x2 - x - 2x + 2)
3x2 - 13x + 12 = 0
3x2 - 9x - 4x + 12 = 0
3x(x - 3) - 4(x - 3) = 0
(3x - 4)(x - 3) = 0
Therefore,
3x - 4 = 0
3x = 4
x = 4/3
Or,
x - 3 = 0
x = 3
Hence, x = 4/3 or x = 3
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