Question

How do you solve `(4x-3)/(x-4)+1=x/(x-3)`?

Answer 1

`x=9/4+i/4*sqrt(3)` or `x=9/4-sqrt(3)/4*i`

Explanation:

Multiplying by `(x-3)(x-4)` we get

`(4x-3)(x-3)+(x-3)(x-4)=x(x-4)`
and this is

`4x^2-18x+21=0`
so we have
`x^2-9/2x+21/4=0`
using the quadratic formula

`x_(1,2)=9/4pm isqrt(3)/4`