Question

Q7. Convert 12/ (V3-v11) into a fraction having a positive rational denominator.​

Answer 1

$\underline{\tt{Answer:}} \\ \\ \tt{Frist\ we\ must\ find\ the\ conjugate\ of\ the\ denominator.}\\ \\ \tt{Conjugate\ of\ \sqrt{3} - \sqrt{11}\ is\ \sqrt{3} + \sqrt{11}.} \\ \\ \tt{Now\ we\ must\ mutiply\ and\ divide\ the\ fraction\ by\ this\ conjugate.}\\ \\ \implies \tt{\dfrac{12}{\sqrt{3} - \sqrt{11}}\ \times \ \dfrac{\sqrt{3} + \sqrt{11}}{\sqrt{3} + \sqrt{11}}\ = \ \dfrac{12\big(\sqrt{3} + \sqrt{11} \big)}{3 - 11 } \ = \ \dfrac{-12\big(\sqrt{3} + \sqrt{11} \big)}{8} }$

$\tt{This\ process\ of \ converting\ irrational\ denominator\ to\ rational}\\ \tt{is\ know\ as\ rationalization.} \\ \\ \tt{The\ rationalized\ fraction\ is: \boxed{\dfrac{-12\big(\sqrt{3} + \sqrt{11} \big)}{8}}}$

Hope this helps : )