Question 1104564
first needs (x+5) in the denominator.
a hole at 7 would require (x-7)/(x-7)
function is (x-7)/(x^2-2x-35)
{{{graph(300,300,-10,10,-10,10,(x-7)/(x^2-2x-35))}}}
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denominator has to exist for all x.  Can use (x^2+1)
numerator has a higher power x, such as x^3.
(2x^3-3x^2+2x-3)/(x^2+1), where the numerator is the product of (x^2+1)(2x-3)-5, the -5 just to show something more than a line. 
{{{graph(300,300,-10,10,-30,10,(2x^3-3x^2+2x-8)/(x^2+1))}}}