Question

qual o conjunto solução de:
$\frac{1}{x} + \frac{1}{x-1} = \frac{3}{2}$

Answer 1

$\frac{1}{x} + \frac{1}{x-1} = \frac{3}{2} \\ \\ mmc=2x(x-1) \\ \\ 2(x-1)+2x=3x(x-1) \\ \\ 2x-2+2x=3x^2-3x \\ \\ 3x^2-3x-2x-2x+2=0 \\ \\ 3x^2-7x+2=0 \\ \\ a=3 \\ b=-7 \\ c=2 \\ \\ \Delta=b^2-4ac \\ \Delta=(-7)^2-4(3)(2) \\ \Delta=49-24 \\ \Delta=25 \\ \\ x= \frac{-b\pm \sqrt{\Delta} }{2a} \\ \\ x= \frac{-(-7)\pm \sqrt{25} }{2.(3)} = \frac{7\pm5}{6} \\ \\ x'= \frac{7+5}{6} = \frac{12}{6} =2 \\ \\ x"= \frac{7-5}{6} = \frac{2}{6} = \frac{1}{3}$