Question

$\frac{X-3}{X-4}+\frac{X-5}{X-6}=\frac{10}{3}WhereX\ne 4,6$

Answer 1

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