solve: x-1/x-2+x-3/x-4=10/3
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0
Step-by-step explanation:
LHS
Taking LCM
(x-1)(x-4) + (x-3)(x-2)/(x-2)(x-4)
(x²-4x-x+4)+(x²-2x-3x+6)/(x²-4x-2x+8)
2x²-10x+10/x²-6x+8
2x²-10x+10/x²-6x+8=10/3
3(2x²-10x+10)=10(x²-6x+8)
6x²-30x+30=10x²-60x+80
-4x²+30x-50=0
-2(2x²-15x+25)=0
(2x²-15x+25)=0
2x²-10x-5x+25=0
2x(x-5)-5(x-5)=0
(2x-5)(x-5)=0
x=5,5/2
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