Question

$\frac{1}{x} - \frac{1}{x + 1} = \frac{1}{6}$
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Answer 1

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

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

$\frac{1}{x} = \frac{(x +1 )}{6(x + 1)} + \frac{(6)}{(x + 1)(6)}$

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

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

$\frac{1}{x} = \frac{x + 7}{6x + 6}$

$1(6x + 6) = (x + 7)(x)$

$6x + 6 = {x}^{2} + 7x$

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

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

r'+r"=-1

r'r"=-6

r'= -3

r"= 2

s={ -3, 2 }