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

Question

1462 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-06-15T08:18:20

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

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

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

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