Question

simplify: (6^-1 - 8^-1)^-1 + (2^-1 - 3^-1)^-1​

Answer 1

Step-by-step explanation:

-6-(-8)+(-2)-(-3)

-6+7-2+3

10-8

2

Answer 2

Step-by-step explanation:

$( {6}^{ - 1} - {8}^{ - 1} ) ^{ - 1} + {( {2}^{ - 1} - {3}^{ - 1} )}^{ - 1} \\ \\ = (\frac{1}{6} - \frac{1}{8} ) ^{ - 1} + ( \frac{1}{2} - \frac{1}{3} ) ^{ - 1} \\ \\ l.c.m \: of \: 6 \: and \: 8 \: is \: 24 \: \: \: \: \: \: \: \: \: \: and \: \: l.c.m \: of \: 2 \: and \: 3 \: is \: 6 \\ \\ = (\frac{(4 - 3)}{24} ) {}^{ - 1} + ( \frac{(3 - 2)}{6} ) {}^{ - 1} \\ \\ = { (\frac{1}{24} )}^{ - 1} + (\frac{1}{6} ) {}^{ - 1} \\ \\ = 24 + 6 \\ \\ = 30 \\ \\ \\ using \: \: \: formula \: \: \: {x}^{ - 1} = \frac{1}{x} \: \: \: \: \: \: \: \: \: and \: \: \: \: \: \: {x}^{ - 2} = \frac{1}{ {x}^{2} }$