Đáp án+Giải thích các bước giải:
`a)x=4-2sqrt3=(sqrt3-1)^2`
`=>A=(sqrt3-1+4)/(sqrt3-1-1)`
`A=(sqrt3+3)/(sqrt3-2)`
`A=((3+sqrt3)(2+sqrt3))/(3-4)`
`A=-(6+3sqrt3+2sqrt3+3)`
`A=-(9+5sqrt3)`
`b)B=(3sqrtx+1)/(x+2sqrtx-3)-2/(sqrtx+3)(x>=0,x ne 1)`
`B=(3sqrtx+1)/((sqrtx-1)(sqrtx+3))-(2sqrtx-2)/((sqrtx-1)(sqrtx+3))`
`B=(sqrtx+3)/((sqrtx-1)(sqrtx+3))`
`B=1/(sqrtx-1)`
`c)A<0`
`<=>1/(sqrtx-1)<0`
Mà `1>0`
`<=>sqrtx-1<0`
`<=>sqrtx<1`
`<=>x<1`
`<=>0<=x<1`.
`d)A/B>x/4+5`
`<=>sqrtx+4>=x/4+5`
`<=>4sqrtx+16>x=+20`
`<=>x-4sqrtx+4<=0`
`<=>(sqrtx-2)^2<=0`
`<=>(sqrtx-2)^2=0`
`<=>sqrtx=2`
`<=>x=4(tmđk)`