Video: Evaluating Rational Functions

Given the function 𝑓(𝑥) = 7/(4𝑥² − 81) + 1/(9𝑥 − 2𝑥²), evaluate 𝑓(3).

02:10

Video Transcript

Given the function 𝑓 of 𝑥 equals seven divided by four 𝑥 squared minus 81 plus one divided by nine 𝑥 minus two 𝑥 squared, evaluate 𝑓 of three.

Well, in order to evaluate 𝑓 of three, we need to substitute 𝑥 equals three into the function 𝑓 of 𝑥. This gives us 𝑓 of three is equal to seven divided by four multiplied by three squared minus 81 plus one divided by nine multiplied by three minus two multiplied by three squared.

If we concentrate on the first fraction, three squared is equal to nine and four multiplied by nine is equal to 36. Therefore, the first fraction becomes seven divided by 36 minus 81 as 36 minus 81 is negative 45. The first fraction simplifies to negative seven 45ths.

The second fraction becomes one divided by 27 minus 18 as nine multiplied by three is 27. Three squared is equal to nine and two multiplied by nine is 18. As 27 take away 18 is nine, the second fraction simplifies to one-ninth. This calculation is the same as negative seven 45ths plus five 45ths as one-ninth is equivalent to five 45ths.

Adding the numerators gives us a final answer of negative two 45ths. This means that the value of 𝑓 of three in the function seven divided by four 𝑥 squared minus 81 plus one divided by nine 𝑥 minus two 𝑥 squared is equal to negative two 45ths.

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