\(\dfrac{1}{\sqrt{x}-1}+\dfrac{\sqrt{x}}{\sqrt{x}+3}-\dfrac{12}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-1\right)}\left(\text{đ}k\text{x}\text{đ}:x\ge0;x\ne1\right)\\ =\dfrac{\sqrt{x}+3}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+3\right)}+\dfrac{\sqrt{x}\left(\sqrt{x}-1\right)}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-1\right)}-\dfrac{12}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-1\right)}\\ =\dfrac{\sqrt{x}+3+x-\sqrt{x}-12}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-1\right)}\\ =\dfrac{x-9}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-1\right)}\\ =\dfrac{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-1\right)}\\ =\dfrac{\sqrt{x}-3}{\sqrt{x}-1}\)
\(=\dfrac{\sqrt{x}+3+\sqrt{x}\left(\sqrt{x}-1\right)-12}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-1\right)}\)
\(=\dfrac{\sqrt{x}-9+x-\sqrt{x}}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-1\right)}=\dfrac{x-9}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-1\right)}\)
\(=\dfrac{\sqrt{x}-3}{\sqrt{x}-1}\)
`(1)/(\sqrt{x}+1)+(\sqrt{x})/(\sqrt{x}+3)-(12)/((\sqrt{x}+3)(\sqrt{x}-1))`
Điều Kiện `x>=0;x\ne1`
`=(\sqrt{x}+3+\sqrt{x}(\sqrt{x}-1)-12)/((\sqrt{x}+3)(\sqrt{x}-1))`
`=(\sqrt{x}+3+x-\sqrt{x}-12)/((\sqrt{x}+3)(\sqrt{x}-1))`
`=(x-9)/((\sqrt{x}+3)(\sqrt{x}-1))`
`=((\sqrt{x}-3)(\sqrt{x}+3))/((\sqrt{x}+3)(\sqrt{x}-1))`
`=(\sqrt{x}-3)/(\sqrt{x}-1)`
