Question

If x= -2/3and y=-3/4, then (x−y)-¹ + (x-¹-y-¹)-¹ is equal to​

Answer 1

$x = - \frac{2}{3} \\ y = - \frac{3}{4} \\ \\ x - y = - \frac{2}{3} + \frac{3}{4} = \frac{ - 8 + 9}{12} \\ = \frac{1}{12} \\ \\ xy = - \frac{2}{3} \times ( - \frac{3}{4} ) \\ = \frac{1}{2} \\ \\ now \\ \: \: \: \: ( {x - y})^{ - 1} + ( {x}^{ - 1} - {y}^{ - 1} ) ^{ - 1} \\ = \frac{1}{x - y} + \frac{xy}{y - x} \\ = \frac{1 - xy}{x - y} \\ = \frac{1 - \frac{1}{2} }{ \frac{1}{12} } \\ = 6$