ĐK: `x>0` 

`A=((\sqrtx)/(\sqrtx+2) - 4/(x+2\sqrtx)):(1+1/(\sqrtx))`

`=((\sqrtx)/(\sqrtx+2)-4/(\sqrtx(\sqrtx+2))):((\sqrtx+1)/(\sqrtx))`

`=(x -4)/(\sqrtx(\sqrtx+2)) . (\sqrtx)/(\sqrtx+1)`

`=((\sqrtx+2)(\sqrtx-2))/(\sqrtx+2) . 1/(\sqrtx+1)`

`=(\sqrt-2)/(\sqrtx+1)`

`A=1/(1.3)+1/(3.5)+....+1/(2009.2011)`

`=> 2A=2/(1.3)+1/(3.5)+...+2/(2009.2011)`

`=1-1/3+1/3+1/5+.....+1/2009-1/2011`

`=1-1/2011`

`=2010/2011`

`=> A=1005/2011`

`3xy(4x-2y)-(x-2y)^3-2(4y^3-1)`

`=12x^2y-6xy^2-(x^3-6x^2y+12xy^2-8y^3)-8y^3+2`

`=12x^2y-6xy^2-x^3+6x^2y-12xy^2+8y^3-8y^3+2`

`=-x^3+18x^2y-18xy^2+2` (??????)

`\sqrt(2+\sqrt3)+\sqrt(2-\sqrt3)`

`=\sqrt((4+2\sqrt3)/2)+\sqrt((4-2\sqrt3)/2)`

`=\sqrt(((\sqrt3)^2+2\sqrt3+1)/2)+\sqrt(((\sqrt3)^2-2\sqrt3+1^2)/2)`

`=\sqrt(((\sqrt3+1)^2)/2)+\sqrt(((\sqrt3-1)^2)/2)`

`=(\sqrt3+1)/(\sqrt2)+(\sqrt3-1)/(\sqrt2)`

`=(2\sqrt3)/(\sqrt2)=\sqrt6`

`(2x-1)^2+2(x-1)(x+1)+(x+1)^2`

`=(2x-1)^2+2(x^2-1)+(x+1)^2`

`=4x^2-4x+1+2x^2-2+x^2+2x+1`

`=7x^2-2x`

- Sửa quyền truy cập file gg drive đi.

- Gửi vào phần trả lời ấy ạ, đừng gửi vào phần reply.

a. `8x+4x^2-12xy=4x(2+x-3y)`

b) `5x^3-10x^2+5x=5x(x^2-2x+1)`

c) `x^3+x^2y-xy^2-y^3=x^2(x+y)-y^2(x+y)=(x+y)(x^2-y^2)=(x+y)^2 (x-y)`

d) `x^2-8x-9=(x^2-2.x.4+4^2)-25=(x-4)^2-5^2=(x+1)(x-9)`

`=111 xx (1+2+3+...+9) + (1001+1003+1005)`

`=111 xx 45 + 3009`

`=4995 +3009`

`=8004`

A