Đáp án:a)$=2\sqrt[]{2}$
b)$=-6-2\sqrt{5}$
Giải thích các bước giải:
$a)\frac{\sqrt{10}-\sqrt{2}}{\sqrt{5}}+\frac{2-\sqrt{2}}{\sqrt{2}-1}$
$=\frac{\sqrt{2}.(\sqrt{5}-1)}{\sqrt{5}-1}+\frac{\sqrt{2}(\sqrt{2}-1)}{\sqrt{2}-1}$
$=\sqrt[]{2}+\sqrt{2}$
$=2\sqrt[]{2}$
$b)(1+\frac{5+\sqrt{5}}{1+\sqrt{5}}).(\frac{5-\sqrt{5}}{1-\sqrt{5}}-1)$
$=(1+\frac{\sqrt{5}(\sqrt{5}+}{1+\sqrt{5}}).(\frac{\sqrt{5}(\sqrt{5}-1)}{1-\sqrt{5}}-1)$
$=(1+\sqrt{5}).(-\sqrt{5}-1)$
$=-(1+\sqrt{5})^2$
$=-6-2\sqrt{5}$
