x-1/x-2+x-3/x-4 = 3 1/2
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Step-by-step explanation:
- x-1/x-2+x-3/x-4=31/2
- (x-2)(x-4)+(x-3)(x-2)/(x-2)(x-4)=31/2 (∵cross multiplication)
- x²-4x-2x+8+x²-2x-3x+6/x²-4x-2x+8=31/2
- 2x²-11x+14/x²-6x+8=31/2
- 2(2x²- 11x+14)=31(x²-6x+8) (again cross multiplication)
- 4x²-22x+28=31x²-186x+248
- 31x²-186x+248-4x²+22x-28=0 (take RHS to LHS )
- 27x²-164x+220=0
- x=28896+√5136/54 and x=28896-√5136/54
(solving 27x²-164x+220=0 by quadratic formula)
i hope it is helpful for you
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