Question

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$frac{1}{sqrt{7}+sqrt{5}}+frac{4}{sqrt{5}+2}- frac{3sqrt{2.5}+sqrt{1.5}}{sqrt{2}}$

Answer 1

$frac{1}{sqrt{7}+sqrt{5}}+frac{4}{sqrt{5}+2}-frac{3sqrt{2.5}+sqrt{1.5}}{sqrt{2}}=\\ frac{1*(sqrt{7}-sqrt{5})}{(sqrt{7}+sqrt{5})*(sqrt{7}-sqrt{5})}+frac{4*(sqrt{5}-2)} {(sqrt{5}+2)*(sqrt{5}-2)}-frac{(3sqrt{2.5}+sqrt{1.5})*sqrt{2}}{sqrt{2}*sqrt{2}}=\\ frac{sqrt{7}-sqrt{5}}{(sqrt{7})^2-(sqrt{5})^2}+frac{4*sqrt{5}-8}{(sqrt{5})^2-2^2}-frac{3sqrt{2.5}*sqrt{2}+sqrt{1.5}*sqrt{2}}{2}=$

$frac{sqrt{7}-sqrt{5}}{7-5}+frac{4*sqrt{5}-8}{5-4}-frac{3sqrt{2.5*2}+sqrt{1.5*2}}{2}=\\ frac{sqrt{7}-sqrt{5}}{2}+frac{4*sqrt{5}-8}{1}-frac{3sqrt{5}+sqrt{3}}{2}=\\ frac{sqrt{7}-sqrt{5}}{2}+frac{8*sqrt{5}-16}{2}-frac{3sqrt{5}+sqrt{3}}{2}=\\ frac{sqrt{7}-sqrt{5}+8*sqrt{5}-16-3sqrt{5}-sqrt{3}}{2}=\\ frac{sqrt{7}+4sqrt{5}-16-sqrt{3}}{2}$