Đáp án+Giải thích các bước giải:

 `a)(3x-1).(x^{2}-2)=0`

`3x-1=0` hoặc `x^{2}-2=0`

`3x=1` hoặc `x^{2}=2`

`x=1/3` hoặc `x^{2}=(\pm\sqrt{2})^{2}`

`x=1/3` hoặc `x=-\sqrt{2}` hoặc `x=\sqrt{2}`

Vậy `S={1/3;-\sqrt{2};\sqrt{2}}`

`b)(x+2).(2x-3)=(x+5).(2x-4)`

`2x^{2}-3x+4x-6=2x^{2}-4x+10x-20`

`2x^{2}-2x^{2}+x-6=6x-20`

`x-6x=-20+6`

`-5x=-14`

`x=14/5`

Vậy `S={14/5}`

`c)(3x-5)^{2}-(2-x)^{2}=0`

`[(3x-5)-(2-x)].(3x-5+2-x)=0`

`(3x-5-2+x).(2x-3)=0`

`(4x-7).(2x-3)=0`

`4x-7=0` hoặc `2x-3=0`

`4x=7` hoặc `2x=3`

`x=7/4` hoặc `x=3/2`

Vậy `S={7/4;3/2}`

`d)\frac{x+3}{x+2}=\frac{6.(x-3)}{x+2}` `(đk : x\ne-2)`

`=>x+3=6.(x-3)`

`6x-18=x+3`

`6x-x=3+18`

`5x=21`

`x=21/5(tmđk)`

Vậy `S={21/5}`

`e)\frac{3}{7-x}+\frac{2}{x+7}=\frac{5}{x^{2}-49}` `(đk: x\ne\pm7)`

`\frac{(-3).(x+7)}{(x-7).(x+7)}+\frac{2.(x-7)}{(x-7).(x+7)}=\frac{5}{(x-7).(x+7)}`

`=>-3x-21+2x-14=5`

`-x-35=5`

`-x=5+35`

`-x=40`

`x=-40(tmđk)`

Vậy `S={-40}`

`g)\frac{1}{x^{2}+5x+6}+\frac{1}{x^{2}+7x+12}+\frac{1}{x^{2}+9x+20}+\frac{1}{x^{2}+11x+30}=1/8`

`(đk: x\ne-2;x\ne-3;x\ne-4;x\ne-5;x\ne-6)`

`\frac{1}{x^{2}+2x+3x+6}+\frac{1}{x^{2}+3x+4x+12}+\frac{1}{x^{2}+4x+5x+20}+\frac{1}{x^{2}+5x+6x+30}=1/8`

`\frac{1}{x.(x+2)+3.(x+2)}+\frac{1}{x.(x+3)+4.(x+3)}+\frac{1}{x.(x+4)+5.(x+4)}+\frac{1}{x.(x+5)+6.(x+5)}=1/8`

`\frac{1}{(x+2).(x+3)}+\frac{1}{(x+3).(x+4)}+\frac{1}{(x+4).(x+5)}+\frac{1}{(x+5).(x+6)}=1/8`

`\frac{1}{x+2}-\frac{1}{x+3}+\frac{1}{x+3}-\frac{1}{x+4}+\frac{1}{x+4}-\frac{1]{x+5}+\frac{1}{x+5}-\frac{1}{x+6}=1/8`

`\frac{1}{x+2}-\frac{1}{x+6}=1/8`

`\frac{8.(x+6)}{8.(x+2).(x+6)}-\frac{8.(x+2)}{8.(x+2).(x+6)}=\frac{(x+2).(x+6)}{8.(x+2).(x+6)}`

`=>8.(x+6))-8.(x+2)=x^{2}+6x+2x+12`

`x^{2}+8x+12=8.(x+6-x-2)`

`x^{2}+8x+12=8.4`

`x^{2}+8x+12-32=0`

`x^{2}+8x-20=0`

`x^{2}+10x-2x-20=0`

`x.(x+10)-2.(x+10)=0`

`(x-2).(x+10)=0`

`x-2=0` hoặc `x+10=0`

`x=2(tmđk)` hoặc `x=-10(tmđk)`

Vậy `S={2;-10}`