Question

QUESTION FOR MODERATORS TO TEST YOUR MATHS ...​

Answer 1

Step-by-step explanation:

$\frac{[ x + \frac{1}{y} ]^{a}[x - \frac{1}{y} ] ^{b} }{[y + \frac{1}{x} ]^{a} [y - \frac{1}{x} ] ^{b} } \\ \\ = \frac{[ \frac{xy + 1}{y} ]^{a}[ \frac{xy - 1}{y} ] ^{b} }{[ \frac{xy + 1}{x} ]^{a} [ \frac{xy - 1}{x} ] ^{b} } \\ \\ = \frac{[ \frac{(xy + 1) ^{a} }{y ^{a} }] [ \frac{(xy - 1) }{y {}^{b} } ] ^{b} }{[ \frac{(xy + 1) {}^{a} }{x {}^{a} } ] [ \frac{(xy - 1) {}^{b} }{x { }^{b} } ] } \\ \\ = \frac{x {}^{a}. {x}^{b} }{ {y}^{a}. {y}^{b} }$

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