Question

Mark (✓) against the correct answer
(6⁻¹ − 8⁻¹)⁻¹=?

(a) $-\frac{1}{2}$
(b) −2
(c) $\frac{1}{24}$
(d) 24

Answer 1

(d) 24

${\left(6^{-1}-8^{-1}\right)}^{-1}={\left(\frac{1}{6}-\frac{1}{8}\right)}^{-1}$
= ${\left(\frac{4-3}{24}\right)}^{-1}$ [since L.C.M. of 6 and 8 is 24]
= ${\left(\frac{1}{24}\right)}^{-1}$
= ${\left(\frac{24}{1}\right)}^1=24$ $\left[s\mathrm{ince}{\left(\frac{a}{b}\right)}^{-1}={\left(\frac{b}{a}\right)}^1\right]$