Final answer:
The equation (x²-4x-5)/(x²+2x) has two vertical asymptotes, which occur when x equals 0 and -2, as these are the values that make the denominator equal to zero without making the numerator zero.
Step-by-step explanation:
The given equation is (x²-4x-5)/(x²+2x). To find if there are vertical asymptotes, we need to determine the values of x for which the denominator equals zero. Since the numerator does not affect the vertical asymptotes of the function, we can focus on the denominator: x²+2x. We can factor this as x(x+2). Setting the factors equal to zero gives us the possible vertical asymptotes: x = 0 and x = -2. However, since these values do not make the numerator zero, it confirms that x = 0 and x = -2 are indeed vertical asymptotes of the function.