Question

Show that [(3/5)^-1 -(1/3)^-1]^-1=-3/4
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Answer 1

Answer:

$({ \frac{3}{5} }^{ - 1} - { \frac{1}{3} }^{ - 1} )^{ - 1} = - \frac{3}{4} \\ \\ lhs \\ = (\frac{5}{3} - \frac{3}{1}) ^{ - 1} \\ = ( \frac{5}{3} - \frac{3 \times 3}{3} )^{ - 1} \\ = (\frac{5}{3} - \frac{9}{3} ) ^{ - 1} \\ = (- \frac{4}{3} ) ^{ - 1} \\ = - \frac{3}{4} \\ \\ therefore \: \\ - \frac{3}{4} = - \frac{3}{4} \ \\ \\ since \: lhs \: = rhs \\ \\ hence \: proved$