Question

rút gọn biểu thức

P=(\(\dfrac{1}{\sqrt{a}-1}-\dfrac{1}{\sqrt{a}}\)):(\(\dfrac{\sqrt{a}+1}{\sqrt{a}-2}\)- \(\dfrac{\sqrt{a}+ 2}{\sqrt{a}-1}\))

Answer 1

Với `a >= 0,a \ne 1;a \ne 4` có:

`P=(1/[\sqrt{a}-1]-1/\sqrt{a}):([\sqrt{a}+1]/[\sqrt{a}-2]-[\sqrt{a}+2]/[\sqrt{a}-1])`

`P=[\sqrt{a}-\sqrt{a}+1]/[\sqrt{a}(\sqrt{a}-1)]:[(\sqrt{a}-1)(\sqrt{a}+1)-(\sqrt{a}+2)(\sqrt{a}-2)]/[(\sqrt{a}-2)(\sqrt{a}-1)]`

`P=1/[\sqrt{a}(\sqrt{a}-1)],[(\sqrt{a}-2)(\sqrt{a}-1)]/[a-1-a+4]`

`P=[\sqrt{a}-2]/[3\sqrt{a}]`