Đáp án:
`a)` `a-b`
`b)` `1-a`
Giải thích các bước giải:
`a)` `{a\sqrt{b}+b\sqrt{a}}/{\sqrt{ab}} : 1/{\sqrt{a}-\sqrt{b}}` `(a;b>0;a\ne b)`
`={\sqrt{ab} . (\sqrt{a}+\sqrt{b})}/\sqrt{ab} . (\sqrt{a}-\sqrt{b})`
`=(\sqrt{a}+\sqrt{b}).(\sqrt{a}-\sqrt{b})`
`=(\sqrt{a})^2-(\sqrt{b})^2`
`=a-b`
$\\$
`b)` `(1+{a+\sqrt{a}}/{\sqrt{a}+1}).(1-{a-\sqrt{a}}/{\sqrt{a}-1})`
`\qquad (a\ge 0;a\ne 1)`
`=[1+{\sqrt{a}.(\sqrt{a}+1)}/{\sqrt{a}+1}].[1-{\sqrt{a}.(\sqrt{a}-1)}/{\sqrt{a}-1}]`
`=(1+\sqrt{a}).(1-\sqrt{a})`
`=1^2-(\sqrt{a})^2`
`=1-a`