Question

Rationalize the denominator of √3-√4/√3+√4-√7
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Answer 1

Answer:  $\frac{-1-\sqrt{21}+\sqrt{28} }{2\sqrt{12} }$

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Step-by-step explanation:

$\frac{\sqrt{3} -\sqrt{4} }{\sqrt{3}+\sqrt{4} - \sqrt{7} }$

$\frac{\sqrt{3} -\sqrt{4} }{\sqrt{3}+\sqrt{4} - \sqrt{7} }*\frac{\sqrt{3} +\sqrt{4}+\sqrt{7} }{\sqrt{3}+\sqrt{4} + \sqrt{7} }$

$\frac{(\sqrt{3} -\sqrt{4})(\sqrt{3}+\sqrt{4} - \sqrt{7}) }{(\sqrt{3}+\sqrt{4})^{2} - (\sqrt{7})^{2} }$

$\frac{3-\sqrt{12}+\sqrt{12}-4-\sqrt{21}+\sqrt{28} }{3+4+2\sqrt{3}.\sqrt{4} - 7 }$

$\frac{-1-\sqrt{21}+\sqrt{28} }{2\sqrt{12} }$