Let S be the set of all real numbers a such that the function (x^2+5x+a)/(x^2+7x-44) can be expressed as the quotient of two linear functions. What is the sum of the elements of S?
Note that x^2 + 7x - 44 can be factored as ( x + 11) ( x - 4)
So x^2 + 5x + a could be ( x + 11) ( x - 6) and a = -66
Or ..... x^2 + 5x + a could be ( x - 4) (x + 9) and a = -36
Note that in the first case the quotient is ( x - 4) /( x - 6)
And in the second case the quotient is ( x + 11) / ( x + 9)
So...S = ( -66, -36) and the sum of its elements is -102