Question

(ETERJ-RJ) A solução da equação
1/2x-3-3/2x²-3x-5/x=0 é


(A)3/2
(B)4/3
(C)-4/3
(D)0
(E)5/3

Answer 1

$\frac{1}{2x-3} -\frac{3}{2x^{2}-3x}-\frac{5}{x}=0\\\\\frac{1}{2x-3} -\frac{3}{x(2x-3)}-\frac{5}{x}=0\\\\\frac{1}{2x-3}-\frac{5}{x}=\frac{3}{x(2x-3)}\\\\Obtenha~o~mmc~do~primeiro~membro~e~fatore:\\\\mmc=x(2x-3)\\\\\frac{x-5(2x-3)}{x(2x-3)}=\frac{3}{x(2x-3)}\\\\Observe~que~os~denominadores~em~ambos~os~membros~sao~iguais\\\\Portanto,~despreze~os~denominadores~e~efetue~as~operacoes:\\\\x-5(2x-3)=3\\\\x-(10x-15)=3~~~~~~~~~atencao~com~os~sinais\\\\x-10x+15=3\\\\-9x=3-15\\\\-9x=-12~.~(-1)\\\\9x=12$

$x=\frac{12}{9}~~~~~~~~~~~~~~~~~~simplifique~por~3\\\\x=\frac{4}{3}\\\\Resposta:~alternativa~(B)~~\frac{4}{3}\\\\\\\\\\\\Bons~estudos~!$