y = (0^2 +4(0)-21)/(0+7) = -21/7 = -3

For a rational function, f(x)/g(x), set f(x) = 0. Solve for x. That gives you possible x intercepts (roots). Check each number (possible x intercept) with the original equation, to make sure it doesn't make the denominator 0. If it does, discard it.

(x+7)(x-3) = 0

x+7 = 0 so x=-7. But - 7 makes the denominator 0, so discard it.

x-3 = 0 so x = 3

x=3 is the only x intercept.