Discussion

If x = 81, then what is the value of

\[ \begin{aligned} &\dfrac{x-6}{x^{3/4}+x^{1/2}} \times \dfrac{x^{1/2}+x^{1/4}}{x^{1/2}+1} \\ &\quad \times x^{1/4} \; ? \end{aligned} \]

Answer: B

With x = 81 the powers are x^(1/4) = 3, x^(1/2) = 9 and x^(3/4) = 27. Substituting these into the expression gives the product below.

\[ \frac{81-6}{27+9} \times \frac{9+3}{9+1} \times 3 \]

\[ = \frac{75}{36} \times \frac{12}{10} \times 3 = 7.5 \]

The value is 7.5. The options 8.5, 6.5 and 5.5 come from small arithmetic slips in the powers of 81.

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