You need to find the roots of the denominator: you can either use the classic {-b \pm \sqrt{b^2-4ac}}/{2a} formula, our you can use this particular one, which is good only if the coefficient of x^2 is 1: in this case, the parabola is of the form x^2+ax+b, and you know that a equals the sum of the roots, but with the opposite sign, while b equals exactly the product of the roots.
So, in this case, we are looking for two roots, which sum up to 2 and which give -15 when multiplied. This numbers are obviously 5 and -3.
Now that you know the roots, you can write down your parabola in a different way: if the roots of ax^2+bx+c are x_0 and x_1, then the following holds:
ax^2+bx+c=(x-x_0)(x-x_1).
In your case, since x_0=5 and x_1=-3, you have that
x^2-2x-15=(x-5)(x+3).
You should see that you can cancel the term (x+3): your fraction can be written as
{x+3}/{x^2-2x-15}=\cancel{x+3}/{(x-5)\cancel((x+3))}=1/{(x-5)}
