Question

The sum of reciprocals of two consecutive integers is 7/12

Answer 1

See the attachment for detail solution
Hope it will help you

Answer 2

let the number be X then
$\frac{1}{x} + \frac{1}{x + 1} = \frac{7}{12} \\ \frac{x + 1 + x}{x(x + 1)} = \frac{7}{12} \\ \frac{2x + 1}{ {x}^{2} + x} = \frac{7}{12} \\ 24x + 12 = 7 {x}^{2} + 7x \\ 7 {x}^{2} - 17x - 12 = 0 \\ {x}^{2} - \frac{17}{7} x - \frac{12}{7} = 0 \\ (x + \frac{4}{7} )(x - 3) = 0 \\ x = - \frac{4}{7} or \: 3$
since x is an integer, the answer is 3,4