Solve the following quadratic equations by factorization:(1/x-2)+(2/x-1)=6/x,x≠0
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x = +3 or +4/3
Step-by-step explanation:
x≠0
1/(x-2) + 2/(x-1) = 6/x
x [ (x-1) + 2(x-2)] = 6 (x-1)(x-2)
x (3x -5) = 6 (x²-3x +2)
3x² -5x = 6x² -18x + 12
3x² -13x + 12 = 0
3x² -9x -4x + 12 = 0
3x (x -3) -4(x - 3) = 0
(3x -4) (x-3) = 0
Therefore x = +3 or +4/3
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