Question 192978
check  how  we  see  the  problem

x/(x-1)+x = 4x-3/(x-1)
mult  thru by (x-1)

x +x(x-1)=4x(x-1)-3
distributing

x+x^2-x=4x^2-4x-3
simplying
x^2=4x^2-4x-3
0=3x^2-4x-3
like  to  factor  but  need  quadratic formula
let  a=3,  b=(-4),  c=(-3)

x=  (-(-4) =/- sqrt ( (-4)^2 -4(3) (-3))/2(3)
x=(4+/- sq rt (16+36))/6
x=(4+/-(7.21))/6
x= 1.869,  or  -.5352    Answer

checking  in  original  eqn  both  match  ok