Question

Resolva a equação de 2°grau:$\frac{1}{x} = \frac{3}{2} - \frac{1}{x-1}$

Answer 1

1/x = 3/2 - 1/ ( x - 1)
mmc = 2x( x - 1)
2(x-1) = 3x( x - 1) - 2x
2x - 2 = 3x² - 3x - 2x
2x - 2 - 3x² + 3x + 2x = 0
-3x² + 7x - 2 = 0
3x² - 7x + 2 = 0
delta = 49 - 24 = 25 ou V25 = +-5***
x = ( 7 +-5)/6
x1 = 12/6 = 2 ****
x2 = 2/6 = 1/3 ****