`#tnvt`
`a)
`\frac{a-4b}{\sqrt{a}-2\sqrt{b}}(a>=0,b>=0,a\ne4b)`
`=\frac{(\sqrt{a}-2\sqrt{b})(\sqrt{a}+2\sqrt{b})}{\sqrt{a}-2\sqrt{b}}`
`=\sqrt{a}+2\sqrt{b}`
`b)`
`\frac{4\sqrt{a}+1}{\sqrt{a}+1}(a>=0)`
`=\frac{4\sqrt{a}+4-3}{\sqrt{a}+1}`
`=1-\frac{3}{\sqrt{a}+1}`
`c)`
`\frac{9-a}{\sqrt{a}-3}(a>=0,a\ne9)`
`=\frac{(3-\sqrt{a])(\sqrt{a}+3)}{-(3-\sqrt{a})}`
`=-\sqrt{a}-3`
`d)`
`(1+\sqrt{x})^2-\frac{4\sqrt{x}}{1-\sqrt{x}}`
`=\frac{(1+\sqrt{x})^2(1-\sqrt{x})-4\sqrt{x}}{1-\sqrt{x}}`
`=\frac{(1-x)(1+\sqrt{x})-4\sqrt{x}}{1-\sqrt{x}}`
`=\frac{1+\sqrt{x}-x-x\sqrt{x}-4\sqrt{x}}{1-\sqrt{x}}`
`=\frac{-x\sqrt{x}-x-3\sqrt{x}+1}{1-\sqrt{x}}`
