Question

what should be subtracted from 7/12+7/8 to obtain the mutiplicative inverse of (4/3-2/9)​

Answer 1

$\frac{4}{3} - \frac{2}{9} = \frac{12 - 2}{9} = \frac{10}{9}$

$\\ now \: \\ \: \: \: \: \: \: \: \: (\frac{7}{12} + \frac{7}{8}) - x = \frac{9}{10} \\ \\ \: \: \: \: \: \: \: \: (\frac{14 + 21}{24}) - x = \frac{9}{10} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \frac{35}{24} - x = \frac{9}{10} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \frac{35}{24} - \frac{9}{10} = x \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x = \frac{175 - 108}{120} = \frac{67}{120}$