Question

$\frac{x}{x + 1} = \frac{8}{3} + \frac{x}{1 - x}$
Me ajudem por favor

Answer 1

MMC : 3.(x+1).(1 - x)

x/(x +1) = 8/3 + x/(1 - x)

[3.x.(1-x)] /[3.(x+1).(1-x)] = [8.(x+ 1).(1 -x) + x.3.(x+1)] /3(x+1).(1 -x)

3x.(1-x) = 8.(x+1).(1-x) + 3x.(x+1)

3x - 3x^2 = 8.(x - x^2 + 1 - x) + 3x^2 + 3x

3x - 3x^2 - 3x^2 - 3x = 8.(- x^2 + 1)

- 6x^2 = - 8x^2 + 8

8x^2 - 6x^2 = 8

2x^2 = 8

x^2 = 8/2

x^2 = 4

x = √4

x = +/- 2

R.: x = 2; x = - 2