Đáp án:
`GTLN_M=2/3<=>x=0.`
Giải thích các bước giải:
`M=(1/(\sqrtx-3)-1/(\sqrtx+3)):3/(\sqrtx-3)(x>=0,x\ne9)`
`M=((\sqrtx+3)/((\sqrtx-3)(\sqrtx+3))-(\sqrtx-3)/((\sqrtx-3)(\sqrtx+3)))*(\sqrtx-3)/3`
`M=((\sqrtx+3-\sqrtx+3)/((\sqrtx-3)(\sqrtx+3)))*(\sqrtx-3)/3`
`M=6/((\sqrtx-3)(\sqrtx+3))*(\sqrtx-3)/3`
`M=2/(\sqrtx+3)`
Vì `x>=0`
`=>\sqrtx>=0`
`=>\sqrtx+3>=3>0`
`=>1/(\sqrtx+3)<=1/3`
`=>2/(\sqrtx+3)<=2/3`
`=>M<=2/3`
Dấu "=" xảy ra khi `x=0.`
Vậy `GTLN_M=2/3<=>x=0.`