Question

simplify each of the following by rationalizing the denominator 2√3-√5/2√2+3√3​

Answer 1

Answer:

hope you have been understood

Answer 2

Step-by-step explanation:

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Answer:

$\frac{2\sqrt{3}-\sqrt{5}}{2\sqrt{2}+3\sqrt{3}}=\frac{18-4\sqrt{6}+2\sqrt{10}-3\sqrt{15}}{19}</p><p>Step-by-step explanation:</p><p>Consider,</p><p>\frac{2\sqrt{3}-\sqrt{5}}{2\sqrt{2}+3\sqrt{3}}</p><p>We multiply and divide by 2√2 - 3√3</p><p>we get,</p><p>\implies\frac{2\sqrt{3}-\sqrt{5}}{2\sqrt{2}+3\sqrt{3}}\times\frac{2\sqrt{2}-3\sqrt{3}}{2\sqrt{2}-3\sqrt{3}}</p><p>\implies\frac{(2\sqrt{3}-\sqrt{5})(2\sqrt{2}-3\sqrt{3})}{(2\sqrt{2}+3\sqrt{3})(2\sqrt{2}-3\sqrt{3})}</p><p>\implies\frac{4\sqrt{6}-6\times3-2\sqrt{10}+3\sqrt{15}}{(2\sqrt{2})^2-(3\sqrt{3})^2}</p><p>\implies\frac{4\sqrt{6}-18-2\sqrt{10}+3\sqrt{15}}{8-27}</p><p>\implies\frac{4\sqrt{6}-18-2\sqrt{10}+3\sqrt{15}}{-19}</p><p>\implies\frac{18-4\sqrt{6}+2\sqrt{10}-3\sqrt{15}}{19$