solve for x: x-1/x-2+x-3/x-4=3 1/3
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Step-by-step explanation:
As given,
(x-1)/(x-2) + (x-3)/(x-4) =10/3
L.C.M. of (x-2) & (x-4) = (x-2)(x-4)
Then,
=> [(x-1)(x-4)+(x-3)(x-2)]/(x-2)(x-4) = 10/3
=> 3(x^2 -5x +4 + x^2 -5x +6) = 10(x-2)(x-4)
=> 3( 2x^2–10x+10) = 10(x^2–6x+8)
=> 6x^2–30x +30 = 10x^2–60x+80
Taking 2 as a common from both sides & cancelling it, we have,
=> 3x^2–15x+15 = 5x^2–30x+40
=>5x^2–3x^2–30x+15x+40–15=0
=> 2x^2 -15x+25= 0
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