Đáp án: + Giải thích các bước giải:
`a)`Ta có:
`VT= ( (1-a\sqrt{a})/(1-\sqrt{a}) +\sqrt{a})( (1-\sqrt{a})/(1-a) )^2`
`=( (1-a\sqrt{a})/(1-\sqrt{a}) +(\sqrt{a}(1-\sqrt{a}))/(1-\sqrt{a}) )( (1-\sqrt{a})/((1-\sqrt{a})(1+\sqrt{a})) )^2`
`= (1-a\sqrt{a}+\sqrt{a}(1-\sqrt{a}))/(1-\sqrt{a}) (1/(1+\sqrt{a}) )^2`
`=(1-a\sqrt{a}+\sqrt{a}-a)/(1-\sqrt{a}) . 1/((1+\sqrt{a})^2)`
`=((1-a)+\sqrt{a}(1-a))/(1-\sqrt{a}) . 1/((1+\sqrt{a})^2)`
`=((1-a)(1+\sqrt{a}))/(1-\sqrt{a}) . 1/((1+\sqrt{a})(1+\sqrt{a})`
`=((1-\sqrt{a})(1+\sqrt{a})(1+\sqrt{a}))/ (1-\sqrt{a}) . 1/((1+\sqrt{a})(1+\sqrt{a})`
`=1 =VP`
`->đpcm`
`b)`Ta có:
`VT = ((x\sqrt{y}+y\sqrt{x})(\sqrt{x}-\sqrt{y}))/(\sqrt{xy})`
`=(\sqrt{xy}(\sqrt{x}+\sqrt{y})(\sqrt{x}-\sqrt{y}))/(\sqrt{xy})`
`=(\sqrt{x}+\sqrt{y})(\sqrt{x}-\sqrt{y})`
`=(\sqrt{x})^2 -(\sqrt{y})^2`
`=x-y =VP`
`-> đpcm`
