Question

Resolva a questão: 2/x-1+1/x-2=2 (equaçao fracionaria)

Answer 1

Resposta:

S={$\frac{3}{2}, 3$}

Explicação passo-a-passo:

$\frac{2}{x-1} +\frac{1}{x-2} =2\\\frac{2(x-2)}{(x-1)(x-2)} +\frac{1(x-1)}{(x-1)(x-2)} =\frac{2(x-1)(x-2)}{(x-1)(x-2)} \\2(x-2)+1(x-1)=2[(x-1)(x-2)]\\2x-4+x-1=2[x^{2} -2x-x+2]\\3x-5=2[x^{2} -3x+2]\\3x-5=2x^{2} -6x+4\\-2x^{2} +3x+6x-5-4=0\\-2x^{2} +9x-9=0\\2x^{2} -9x+9=0\\\\Delta = b^{2} -4ac\\\\Delta=(-9)^{2} -4.2.9\\Delta = 81-72\\Delta = 9\\\\x=\frac{-b+-\sqrt{Delta} }{2a} \\x=\frac{9+-3}{4} \\x'=\frac{9+3}{4} =\frac{12}{4} =3\\x''=\frac{9-3}{4}=\frac{6}{4}  =\frac{3}{2}$