Question

$\frac{1}{x} + \frac{1}{x + 1} = \frac{5}{6}$
alguem me ajudaaaa​

Answer 1

Olá, tudo bem ?

Veja a resolução abaixo ⇩

$\frac{1}{x} + \frac{1}{x + 1} = \frac{5}{6}$

$\frac{1}{x} + \frac{1}{x + 1} = \frac{5}{6},x\neq0,x\neq - 1$

$\frac{1}{x} + \frac{1}{x + 1} - \frac{5}{6} = 0$

$\frac{6(x + 1) + 6x - 5x \times (x + 1)}{6 x \times (x + 1)} = 0$

$\frac{6x + 6 + 6x - 5x \times (x + 1)}{6x \times (x + 1)}$

$\frac{6x + 6 + 6x - 5 {x}^{2} - 5x }{6x \times (x + 1)}$

$\frac{7x + 6 - 5 {x}^{2} }{6x \times (x + 1)} = 0$

$7x + 6 - 5 {x}^{2} = 0$

$- 5 {x}^{2} + 7x + 6 = 0$

$5 {x}^{2} - 7x - 6 = 0$

$5 {x}^{2} + 3x - 10x - 6 = 0$

$x \times (5x + 3) - 10x - 6 = 0$

$x \times (5x + 3) - 2(5x + 3) = 0$

$(5x + 3) \times (x - 2) = 0$

$5x + 3 = 0 \\ x - 2 = 0$

$x = - \frac{3}{5} \\ \: \: \: x - 2 = 0$

$x = - \frac{3}{5} ,x\neq0 \: ,x\neq - 1 \\ x = 2 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

$x = - \frac{3}{5} \\ x = 2 \: \: \: \: \:$

$\boxed{\boxed{\red { x_{1} = - \frac{3}{5}, x_{2} = 2 }}} {\green{ \: ⇒resposta✓}}$

Espero ter colaborado, bons estudos❤.