Đáp án+Giải thích các bước giải:

 `a)`

`A=1/(1+\sqrt{2})+1/(\sqrt{2}+\sqrt{3})+...+1/(\sqrt{n}+\sqrt{n+1})`

`A=(1-\sqrt{2})/((1-\sqrt{2})(1+\sqrt{2}))+(\sqrt{2}-\sqrt{3})/((\sqrt{2}+\sqrt{3})(\sqrt{2}-\sqrt{3}))+...+(\sqrt{n}-\sqrt{n+1})/((\sqrt{n}-\sqrt{n+1})/(\sqrt{n}+\sqrt{n+1}))`

`A=(1-\sqrt{2})/(1-2)+(\sqrt{2}-\sqrt{3})/(2-3)+,....+(\sqrt{n}-\sqrt{n+1})/(n-n-1)`

`A=\sqrt{2}-1+\sqrt{3}-\sqrt{2}+....+\sqrt{n+1}-\sqrt{n}`

`A=\sqrt{n+1}-1`

`b)`

`B=(1/(a-\sqrt{a})+1/(\sqrt{a}-1)):(\sqrt{a}+1)/(a-2\sqrt{a}+1)` vói `a>=0;ane1`

`B=(1/(\sqrt{a}(\sqrt{a}-1))+1/(\sqrt{a}-1)):(\sqrt{a}+1)/(\sqrt{a}-1)^2`

`B=(1+\sqrt{a})/(\sqrt{a}(\sqrt{a}-1)):(\sqrt{a}+1)/(\sqrt{a}-1)^2`

`B=(1+\sqrt{a})/(\sqrt{a}(\sqrt{a}-1))*(\sqrt{a}-1)^2/(\sqrt{a}+1)`

`B=(1+\sqrt{a})/(\sqrt{a}(\sqrt{a}-1))*(\sqrt{a}-1)^2/(\sqrt{a}+1)`

`B=(\sqrt{a}-1)/\sqrt{a}`