Find all values of x such that \frac{x}{x - 5} = \frac{4}{x - 4} + \frac{3}{x} - 2.
xx−5=4x−4+3x−2xx−5=7x−12−2x(x−4)x(x−4)=−2x2+15x−12x2−4xx3−4x2=(x−5)(−2x2+15x−12)x3−4x2=−2x3+25x2−87x+603x3−29x2+87x−60=0
Solving numerically (or using Cardano's formula or Tartaglia's formula) we have x≈0.97404 or x≈4.3463±1.2816i