Question

x-2\x-3+x-4\x-5=10\3,xis not equals to 3,5

Answer 1

Answer:

X=7/2 and 6

Step-by-step explanation:

(x-2)/(x-3) +(x-4)/(x-5) =10/3

on adding

{(x-2)(x-5)+(x-4)((x-3)}/(x-3)(x-5) =10/3l

{(x^2 -7x +10)+(x^2-7x +12)}/(x-3)(x-5) =10/3

(2x^2-14x +22)/(x^2-8x+15)=10/3

cross multiply

3(2x^2-14x+22) =10(x^2-8x+15)

6x^2 -42x+ 66=10x^2 -80x +150

on transposition...

6x^2-10x^2 -42x+80x+66-150=0

-4x^2 +38x - 84=0

divide both side by (-2)

2x^2-19x+42=0

on factorisinig

42×2=84

prime factors of 84=2×2×3×7

12×7=84

12+7=19

so we take 12and 7

2x^2 -12x -7x +42 =0

2x(X-6)-7(x-6)=0

2x-7=0 orx-6=0

X=7/2 or X=6

so X=7/2 and 6 both satisfied in given question

ans X=7/2 and 6