Question

Resolva a equação: 2/× = x-1/x+2 Ficaria muito agradecida se alguém pudesse me ajudar!

Answer 1

Explicação passo-a-passo:

$\dfrac{2}{x}=\dfrac{x-1}{x+2}$

$x\cdot(x-1)=2\cdot(x+2)$

$x^2-x=2x+4$

$x^2-x-2x-4=0$

$x^2-3x-4=0$

$\Delta=(-3)^2-4\cdot1\cdot(-4)$

$\Delta=9+16$

$\Delta=25$

$x=\dfrac{-(-3)\pm\sqrt{25}}{2\cdot1}=\dfrac{3\pm5}{2}$

$x'=\dfrac{3+5}{2}~\longrightarrow~x'=\dfrac{8}{2}~\longrightarrow~x'=4$

$x"=\dfrac{3-5}{2}~\longrightarrow~x"=\dfrac{-2}{2}~\longrightarrow~x"=-1$

$S=\{-1,4\}$

Answer 2

Oie, Td Bom?!

$\frac{2}{x} = \frac{x - 1}{x + 2} \\ \\ \frac{2(x + 2)}{x} = x - 1 \\ \\ 2(x + 2) = (x - 1)x \\ \\ 2(x + 2) - (x - 1)x = 0 \\ \\ 2x + 4 - (x {}^{2} - x) = 0 \\ \\ 2x + 4 - x {}^{2} + x = 0 \\ \\ 3x + 4 - x {}^{2} = 0 \\ \\ - x {}^{2} + 3x + 4 = 0 \\ \\ x {}^{2} - 3x - 4 = 0 \\ \\ x {}^{2} + x - 4x - 4 = 0 \\ \\ x \: . \: (x + 1) - 4(x + 1) = 0 \\ \\ (x + 1) \: . \: (x - 4) = 0$

$x + 1 = 0⟶x = - 1 \\ x - 4 = 0⟶x = 4$

S = $\left \{x_{1} = - 1 \: , \: x_{2} = 4 \right \}$

Att. Makaveli1996