Question 683680
<pre>
There is a typo, for there are no such consecutive integers.  I am guessing
that the 25/56 should have been 15/56.  I will assume that.

Smaller integer = x
Larger integer = x+1

                   {{{1/x}}}{{{""+""}}}{{{1/(x+1)}}}{{{""=""}}}{{{15/56}}}

Multiply through by LCD of 56x(x+1), written as {{{expr(56x(x+1)/1)*""}}}

       {{{expr(56x(x+1)/1)*""}}}{{{1/x}}}{{{""+""}}}{{{expr(56x(x+1)/1)*""}}}{{{1/


       (x+1)}}}{{{""=""}}}{{{expr(56x(x+1)/1)*""}}}{{{15/56}}}

     {{{expr(56cross(x)(x+1)/1)*""}}}{{{1/cross(x)}}}{{{""+""}}}{{{expr(56x(cross(x+1))/1)*""}}}{{{1/(cross(x+1))}}}{{{""=""}}}{{{expr(cross(56)x(x+1)/1)*""}}}{{{15/cross(56)}}}
   
             56(x+1) + 56x = 15x(x+1)

            56x + 56 + 56x = 15x² + 15x

                 112x + 56 = 15x² + 15x
                         0 = 15x² - 97x - 56
                         0 = (x - 7)(15x + 8)
             
                       x - 7 = 0;   15x + 8 = 0
                           x = 7        15x = -8
                                          x = {{{-8/15}}}

Ignore the fraction answer.

Thus the integers are x = 7 and x+1 = 8

Edwin</pre>