Question

1/x-1=3/x+2-2/x-3 como resolver essa equação fracionaria com incógnita

Answer 1

Olá!

$\dfrac{1}{x-1}~=~\dfrac{3}{x+2}~-~\dfrac{2}{x-3}\\ \\ \\\\ \dfrac{(x+2).(x-3)}{(x-1).(x+2).(x-3)} ~ =~\dfrac{\left[\33.(x-1).(x-3)]~-~\left[\22.(x-1).(x+2)]}{(x-1).(x+2).(x-3)} \\ \\ \\ \\ x^{2}-3x+2x-6~=~3x^{2}-9x-3x+9-2x^{2}-4x+2x+4\\ \\ \\ x^{2}-x-6~=~x^{2}-14x+13\\ \\ \\ x^{2}-x-6-x^{2}+14x-13=0\\ \\ \\ 13x-19=0\\ \\ \\ \\ \boxed{x=\dfrac{19}{13}}$

:)