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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.
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Well, in order to evaluate 𝑓 of three, we need to substitute 𝑥 equals three into the function 𝑓 of 𝑥.
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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.
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If we concentrate on the first fraction, three squared is equal to nine and four multiplied by nine is equal to 36.
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Therefore, the first fraction becomes seven divided by 36 minus 81 as 36 minus 81 is negative 45.
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The first fraction simplifies to negative seven 45ths.
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The second fraction becomes one divided by 27 minus 18 as nine multiplied by three is 27.
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Three squared is equal to nine and two multiplied by nine is 18.
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As 27 take away 18 is nine, the second fraction simplifies to one-ninth.
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This calculation is the same as negative seven 45ths plus five 45ths as one-ninth is equivalent to five 45ths.
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Adding the numerators gives us a final answer of negative two 45ths.
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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.