Respostas

2014-04-14T20:31:09-03:00
x-1/2=x/x+2, multiplicando os extremos obtemos:
2.x = (x-1)(x+2) => 2x = x
² + 2x - x - 2 => x² - x - 2 =0 // a = 1; b = -1 e c = -2
Δ = b² - 4ac = (-1)² - 4.1.(-2) = 1 + 8 = 9
x' = -b + √Δ/2a = (1 + 3)/2 = 4/2 = 2
x" = -b - √Δ/2a = (1 - 3)/2 = -2/2 = -1 ===>> S (-1, 2)
2014-04-14T20:33:58-03:00
 \frac{x-1}{2} =  \frac{x}{x+2}
2x = ( x - 1 ) . ( x + 2 )
2x = x² + 2x - x - 2
x² - x - 2 = 0

Agora resolveremos por bhaskara

Δ = b² - 4 ac
Δ = ( - 1 )² - 4 . 1 . ( - 2 )
Δ = 1 + 8
Δ = 9

x1 = -b + √Δ / 2 a
x1 = - ( - 1 ) + √9 / 2
x1 = 1 + 3 / 2
x1 = 4 / 2
x1 = 2

x2 = -b - √Δ / 2 a
x2 = - ( - 1 ) - √9 / 2
x2 = 1 - 3 / 2
x2 = 2 / 2
x2 = 1

Se tivermos x = 1, a igualdade sera um absurdo, pois:

\frac{1-1}{2} = \frac{x1}{1+2}
\frac{0}{2} = \frac{1}{3}

Agora se x = 2

\frac{2-1}{2} = \frac{2}{2+2}
\frac{1}{2} = \frac{2}{4}
\frac{1}{2} = \frac{1}{2}

Portanto, x = 2