6/x-2/x-1=1/x-2 solve this fast
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Solution :
6/x - 2/( x - 1 ) = 1/( x - 2 )
=> [6(x-1)-2x]/[x(x-1)] = 1/(x-2)
=> (6x-6-2x)/(x²-x) = 1/(x-2)
=> (4x-6)(x-2) = x²-x
=> 4x² - 8x - 6x + 12 = x² - x
=> 4x² - x² - 14x + x + 12 = 0
=> 3x² - 13x + 12 = 0
=> 3x² - 9x - 4x + 12 = 0
=> 3x( x - 3 ) - 4( x - 3 ) = 0
=> ( x - 3 )( 3x - 4 ) = 0
=> x - 3 = 0 or 3x - 4 = 0
=> x = 3 or x = 4/3
•••••
6/x - 2/( x - 1 ) = 1/( x - 2 )
=> [6(x-1)-2x]/[x(x-1)] = 1/(x-2)
=> (6x-6-2x)/(x²-x) = 1/(x-2)
=> (4x-6)(x-2) = x²-x
=> 4x² - 8x - 6x + 12 = x² - x
=> 4x² - x² - 14x + x + 12 = 0
=> 3x² - 13x + 12 = 0
=> 3x² - 9x - 4x + 12 = 0
=> 3x( x - 3 ) - 4( x - 3 ) = 0
=> ( x - 3 )( 3x - 4 ) = 0
=> x - 3 = 0 or 3x - 4 = 0
=> x = 3 or x = 4/3
•••••
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