Đáp án + Giải thích các bước giải:
a)
`C=1/(\sqrtx+1)-3/(x\sqrtx+1)+2/(x-\sqrtx+1)(x\ge0)`
`=>C=(x-\sqrtx+1)/((\sqrtx+1)(x-\sqrtx+1))-3/(x\sqrtx+1)+(2(\sqrtx+1))/((x-\sqrtx+1)(\sqrtx+1))`
`=>C=(x-\sqrtx+1-3+2\sqrtx+2)/(x\sqrtx+1)`
`=>C=(x+\sqrtx)/(x\sqrtx+1)`
`=>C=(\sqrtx(\sqrtx+1))/((\sqrtx+1)(x-\sqrtx+1))`
`=>C=(\sqrtx)/(x-\sqrtx+1)`
b)
Thay `x=6-2\sqrt5` vào `C` ta có:
`C=(\sqrt{6-2\sqrt5})/(6-2\sqrt5-\sqrt{6-2\sqrt5}+1)`
`=>C=(\sqrt{5-2\sqrt5+1})/(7-2\sqrt5-\sqrt{5-2\sqrt5+1})`
`=>C=(\sqrt{(\sqrt5-1)^2})/(7-2\sqrt5-\sqrt{(\sqrt5-1)^2})`
`=>C=(|\sqrt5-1|)/(7-2\sqrt5-|\sqrt5-1|)`
`=>C=(\sqrt5-1)/(7-2\sqrt5-\sqrt5+1)`
`=>C=(\sqrt5-1)/(8-3\sqrt5)`
