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Give an example of a rational expression P/Q such that: The degree of the denominator Q is 3 and this expression is defined for all real numbers except the values 2 and 4.

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We need the denominator to be a polynomial of degree 3, hence it has three roots.

Let these roots be a, b and c

Then:

Q = (x-a)(x-b)(x-c)

Now, no one says that the roots can not have multiplicity. For example (x-1)^3 ...

Solution Summary

An example is given of a rational expression P/Q such that: The degree of the denominator Q is 3 and this expression is defined for all real numbers except the values 2 and 4.

$2.19