Which of the following is the graph of the rational function? y=x^2+2x-8/x^2-9

Notice that we can simplify both numerator and denominator of our rational function. In the numerator we have a quadratic expression of the form . To to simplify it, we are going to find tow numbers that add to 2 and multiply to -8; those numbers are 4 and -2.

In the denominator we have a difference of squares:


Now we can rewrite our function:


From the simplified form of our rational function we can infer that its graph has two vertical asymptotes at  and 

We can conclude that the graphic of our rational function is: