Question 76

$$\frac{\left(x + \frac{1}{y}\right)^a . \left(x - \frac{1}{y}\right)^b}{\left(y + \frac{1}{x}\right)^a . \left(y - \frac{1}{x}\right)^b} =$$

Solution

$$\left(\frac{x + \frac{1}{y}}{y + \frac{1}{x}}\right)^a\left(\frac{x - \frac{1}{y}}{y - \frac{1}{x}}\right)^b$$

$$= \left(\frac{xy + 1}{xy + 1} \times \frac{x}{y}\right)^a \left(\frac{xy - 1}{xy - 1} \times \frac{x}{y}\right)^b$$

$$= \left(\frac{x}{y}\right)^a \left(\frac{x}{y}\right)^b$$

$$= \left(\frac{x}{y}\right)^{a+b}$$

Hence the answer is option A

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