Section 1.3 : Radicals
19. Rationalize the denominator. Assume that \(x\) is positive.
\[\frac{{10}}{{3 - 5\sqrt x }}\] Show SolutionFor this problem we need to multiply the numerator and denominator by \(3 + 5\sqrt x \) in order to rationalize the denominator.
\[\frac{{10}}{{3 - 5\sqrt x }} = \frac{{10}}{{3 - 5\sqrt x }}\frac{{3 + 5\sqrt x }}{{3 + 5\sqrt x }} = \frac{{10\left( {3 + 5\sqrt x } \right)}}{{\left( {3 - 5\sqrt x } \right)\left( {3 + 5\sqrt x } \right)}} = \require{bbox} \bbox[2pt,border:1px solid black]{{\frac{{30 + 50\sqrt x }}{{9 - 25x}}}}\]