Question

Verify that $(x÷$y)^{-1} =$x^{-1}÷y^{-1}$, if $x=\frac{-15}{26},y=\frac{5}{13}$ [4 MARKS]

Answer 1

Concept : 1 Mark
Calculation : 2 Marks
Conclusion : 1 Mark

$x=\frac{-15}{26},y=\frac{5}{13}$

$LHS=(x÷y{)}^{-1}$

$={(\frac{-15}{26}÷\frac{5}{13})}^{-1}$

$={(\frac{-15}{26}\times \frac{13}{5})}^{-1}$

$={\left(\frac{-3}{2}\right)}^{-1}$

$=\frac{-2}{3}.........\left(i\right)$

$RHS=x^{-1}÷y^{-1}$

$={\left(\frac{-15}{26}\right)}^{-1}÷{\left(\frac{5}{13}\right)}^{-1}$

$=\left(\frac{-26}{15}\right)÷\left(\frac{13}{5}\right)$

$=\frac{-26}{15}\times \frac{5}{13}$

$=\frac{-2}{3}........\left(ii\right)$

From (i) and (ii) LHS = RHS.
Hence verified.