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Why must we always be mindful of the final value of the denominator in a rational expression?

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What is the main danger you can encounter in the denominator? What is the 1 value you absolutely cannot have? Thats right, zero. your denominator cant be zero and still have a continuous function.
So your equation in particular, you need to concentrate on what values of x will give a value of zero in the denominator. You can use the quadratic formula or you can factor the polynomial. either way you will find that the denominator will be zero when x= 4 and -4.