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CaHeK987 [17]
3 years ago
6

Can someone help me answer this?

Mathematics
1 answer:
grin007 [14]3 years ago
8 0

Answer:

The function f(x) has a hole at point x = - 5.

Step-by-step explanation:

We are given a function as

f(x) = \frac{x^{2} + 7x + 10}{x^{2} + 9x + 20}

Now, we have to describe where the function has a hole.

Now, f(x) = \frac{x^{2} + 7x + 10}{x^{2} + 9x + 20}

⇒ f(x) = \frac{(x + 5)(x + 2)}{(x + 4)(x + 5)}

Therefore, the common factor of the numerator and denominator is (x + 5).

Now, (x + 5) = 0

⇒ x = - 5

Therefore, the function f(x) has a hole at point x = - 5. (Answer)

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