x-1/x-2 + x-3/x-4 = 10 /3 .....dis is de given equation..
u mus take de LCM
i.e. (x-1)(x-4) / (x-2) (x-4) = 10/3
i.e. x2-4 - x + 4 +x2 -2x - 3x +6 / x2 -4x - 2x +8 =10/3
i.e. 2x2 - 10x +10 / x2 - 6x +8 = 10/3
wen u cross multiply..u get..
3 ( 2x2 - 10x + 10) = 10(x2 - 6x + 8)
we get de final equation as ... -4x2 + 30x - 50 = 0
takin de common factor... we get de equation as... -2x2 + 15x - 25 = 0
we must multiply -1 on both de sides of de equation...
so de equation wil b..... 2x2 - 15x +25 = 0
usin de factorisation method we get.... (x2 -10x) (-5x+25) = 0
i.e . 2x(x-5) -5(x-5) = 0
i.e. (x-5)(2x-5) = 0...
which implies dat the roots of dis equation are...2x-5=0 i.e. 5/2
and x-5 = 0 ..i.e.5
hence de roots are 5/2 and 5
i hope this helps u ..if it did thumbs up plz!!!!!!!!!!