x-3/x-4+x-5/x-6=10/6
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x-3/x-4 + x-5/x-6=10/6
[(x-3)(x-6)+(x-5)(x-4)]/(x-4)(x-6) =5/3
(x^2-9x+18+x^2-9x+20)/(x^2-10x+24)=5/3
(2x^2-18x+38)/(x^2-10x+24)=5/3
3(2x^2-18x+38)=5(x^2-10x+24)
6x^2-54x+114=5x^2-50x+120
6x^2-54x+114-5x^2+50x-120=0
x^2-4x-6=0
compare above equation with ax^2+bx+c=0
a=1,b=-4,c=-6
by formula
x=2+ root10 or 2- root10
[(x-3)(x-6)+(x-5)(x-4)]/(x-4)(x-6) =5/3
(x^2-9x+18+x^2-9x+20)/(x^2-10x+24)=5/3
(2x^2-18x+38)/(x^2-10x+24)=5/3
3(2x^2-18x+38)=5(x^2-10x+24)
6x^2-54x+114=5x^2-50x+120
6x^2-54x+114-5x^2+50x-120=0
x^2-4x-6=0
compare above equation with ax^2+bx+c=0
a=1,b=-4,c=-6
by formula
x=2+ root10 or 2- root10
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