Question 585854
Let the positive integer be x.

Reciprocal of the integer would be = {{{ 1/x }}}

Now, we can set up the equation as:

{{{ x + 5 = 36 * (1/x) }}}
or {{{ x*(x+5) = 36 }}}   {Multiplying both the sides by x}
{{{ x^2 + 5x = 36 }}}
{{{ x^2 + 5x -36 = 0 }}}
{{{ x^2 + 9x - 4x - 36 = 0}}}  { Factoring by regrouping}
{{{ x(x+9) - 4(x +9) =0 }}}
{{{ (x+9)(x-4) =0 }}}
{{{ x=-9, x =4}}}
Since we have assumed that the integer is positive or x > 0
Therefore, x =4

Hope this helps~!