The dnominator of the rational expression has to be such that
when either -4 or -7 is substituted for x, the denominator
becomes zero.  So we find such a denominator we find a quadratic
equation with solutions 

    x = -4 and x = -7 

Get 0 on the right of each:

   x+4 = 0 and x+7 = 0

Now we multiply equals by equals,
multiply left sides and multiply right sides:

  (x+4)(x+7) = (0)(0)

  (x+4)(x+7) = 0 

So that can be the denominator of such a rational 
function.  The numerator can be anything you choose:

 or  or 

or any numerator you want to make up, as long is it doesn't contain
another variable besides x.  You can even multiply the denominator by
any constant, like this



Edwin