`(2)/(3)xx(20)/(21)xx(3)/(2)xx(7)/(5)`

`=(2xx20xx3xx7)/(3xx21xx2xx5)`

`=(2xx5xx4xx3xx7)/(3xx3xx7xx2xx5)`

`=(4)/(3)`

``

`(5)/(17)xx(21)/(32)xx(47)/(24)xx0`

`=0`

``

`(11)/(3)xx(26)/(7)-(26)/(7)xx(8)/(3)`

`=(26)/(7)xx((11)/(3)-(8)/(3))`

`=(26)/(7)xx(3)/(3)`

`=(26)/(7)xx1=26/7`

`(2)/(5)xx(25)/(29)+(3)/(5)xx(25)/(29)`

`=(25)/(29)xx((2)/(5)+(3)/(5))`

`=(25)/(29)xx(5)/(5)`

`=(25)/(29)xx1=25/29`

``

`(5)/(2)xx(3)/(7)-(3)/(14):(6)/(7)`

`=(5xx3)/(2xx7)-(3)/(14)xx(7)/(6)`

`=(15)/(14)-(3xx7)/(2xx7xx2xx3)`

`=(15)/(14)-(1)/(2xx2)`

`=(15)/(14)-(1)/(4)`

`=(15xx2-1xx7)/(28)`

`=(23)/(28)`

``

`(15)/(4):(5)/(12)-(6)/(5):(11)/(15)`

`=(15)/(4)xx(12)/(5)-(6)/(5)xx(15)/(11)`

`=(15)/(5)xx(12)/(4)-(15)/(5)xx(6)/(11)`

`=(15)/(5)xx((12)/(4)-(6)/(11))`

`=3xx(3-(6)/(11))`

`=9-3xx(6)/(11)`

`=(9xx11-18)/(11)`

`=(81)/(11)`

`(a):\  a=16(TMDK)=>A=(\sqrt{16}+1)/(\sqrt{16}-3)=(4+1)/(4-3)=5`

`(b):\ B=(2\sqrt{a})/(\sqrt{a}+3)+(\sqrt{a})/(\sqrt{a}-3)-(3a+3)/((\sqrt{a}-3)(\sqrt{a}+3))\    (a\ge0;a\ne 9)`

`=(2\sqrt{a}(\sqrt{a}-3)+\sqrt{a}(\sqrt{a}+3)-(3a+3))/((\sqrt{a}-3)(\sqrt{a}+3))`

`=(2a-6\sqrt{a}+a+3\sqrt{a}-3a-3)/((\sqrt{a}-3)(\sqrt{a}+3))`

`=(-3\sqrt{a}-3)/((\sqrt{a}-3)(\sqrt{a}+3))`

``

`P=A/B\  (ĐK:x\ge 0;x\ne 9)`

`=(\sqrt{a}+1)/(\sqrt{a}-3):(-3(\sqrt{a}+1))/((\sqrt{a}-3)(\sqrt{a}+3))`

`=(\sqrt{a}+1)/(\sqrt{a}-3).((\sqrt{a}-3)(\sqrt{a}+3))/(-3(\sqrt{a}+1))`

`=-(\sqrt{a}+3)/(3)`

`(c):\  P-1=-(\sqrt{a}+3)/(3)-1=(-\sqrt{a}-3-3)/(3)`

`=(-\sqrt{a}-6)/(3)=-(\sqrt{a}+6)/(3)`

Vì : `\sqrt{a}+6 \ge 6>0` với mọi `x\in ĐK`

`=>(\sqrt{a}+6)/(3) >0`

`=>-(\sqrt{a}+6)/(3)<0`

Hay `P-1<0` 

Vậy `P<1`

`x+(-3)/(7)=(-7)/(2)+(-3)/(7)`

`=>x=(-7)/(2)+(-3)/(7)+(3)/(7)`

`=>x=(-7)/(2)+(-3+3)/(7)`

`=>x=(-7)/(2)+(0)/(7)`

`=>x=-7/2`

`(a):\  (x+1)(x^{2}-x+1)-(x^{3}-1)`

`=x^{3}+1^{3}-x^{3}+1`

`=2`

`(b):\  (x-y)^{2}-(x+y)^{2}`

`=x^{2}-2xy+y^{2}-(x^{2}+2xy+y^{2})`

`=-4xy`

`(c):\  (x-2)(x^{2}+2x+4)+(1-x)(x^{2}+x+1)`

`=x^{3}-2^{3}+1^{3}-x^{3}`

`=-8+1=-7`

`-(2)/(3).x+0,2=(-(1)/(2))^{2}`

`=>-(2)/(3)x+(2)/(10)=(1)/(4)`

`=>-(2)/(3)x=(1)/(4)-(2)/(10)=(5)/(20)-(4)/(20)`

`=>-(2)/(3)x=1/20`

`=>x=(1)/(20):(-(2)/(3))=(1)/(20).(-(3)/(2))`

`=>x=-3/40`

`(a):\  (\sqrt{99}-\sqrt{18}+\sqrt{11}).\sqrt{11}+3\sqrt{22}`

`=(\sqrt{9}.\sqrt{11}-\sqrt{9}.\sqrt{2}+\sqrt{11}).\sqrt{11}+3\sqrt{22}`

`=3.\sqrt{11}^{2}-3.\sqrt{2}.\sqrt{11}+\sqrt{11}^{2}+3\sqrt{22}`

`=3.11-3.\sqrt{22}+11+3\sqrt{22}`

`=33+11=44`

`(b):\  \sqrt{4+2\sqrt{3}}+\sqrt{4-2\sqrt{3}}`

`=\sqrt{3+2\sqrt{3}+1}+\sqrt{3-2\sqrt{3}+1}`

`=\sqrt{(\sqrt{3}+1)^{2}}+\sqrt{(\sqrt{3}-1)^{2}}`

`=|\sqrt{3}+1|+|\sqrt{3}-1|`

`=\sqrt{3}+1+\sqrt{3}-1`

`=2\sqrt{3}`

`(c):\  (5)/(\sqrt{7}+\sqrt{2})-(7-\sqrt{7})/(\sqrt{7}-1)+6\sqrt{1/2}`

`=(5(\sqrt{7}-\sqrt{2}))/((\sqrt{7}-\sqrt{2})(\sqrt{7}+\sqrt{2}))-(\sqrt{7}(\sqrt{7}-1))/(\sqrt{7}-1)+(6)/(\sqrt{2})`

`=(5(\sqrt{7}-\sqrt{2}))/(7-2)-\sqrt{7}+(6\sqrt{2})/(2)`

`=\sqrt{7}-\sqrt{2}-\sqrt{7}+3\sqrt{2}`

`=2\sqrt{2}`

`(11)/(23.34)+(11)/(34.45)+...+(11)/(90.101)+x=(-1)/(101)`

`=>(34)/(23.34)-(23)/(23.34)+(45)/(34.45)-(34)/(34.45)+...+(101)/(90.101)-(90)/(90.101)+x=(-1)/(101)`

`=>(1)/(23)-(1)/(34)+(1)/(34)-(1)/(45)+...+(1)/(90)-(1)/(101)+x=(-1)/(101)`

`=>(1)/(23)-(1)/(101)+x=(-1)/(101)`

`=>(1)/(23)+x=(-1)/(101)+(1)/(101)`

`=>x+(1)/(23)=0`

`=>x=-1/23`

`27x^{3}-1`

`=(3x)^{3}-1^{3}`

`=(3x-1)[(3x)^{2}+3x+1^{2}]`

`=(3x-1)(9x^{2}+3x+1)`

`x^{2}(3x+1)-(x-3)^{2}=-9`

`<=>3x^{3}+x^{2}-(x^{2}-6x+9)=-9`

`<=>3x^{3}+x^{2}-x^{2}+6x-9=-9`

`<=>3x^{3}+6x=0`

`<=>x(3x^{2}+6)=0`

`=>x=0` hoặc `3x^{2}+6=0` (Loại . Vì : `3x^{2}+6\ge6 >0` với mọi `x`)

Vậy `S={0}`