Đáp án+Giải thích các bước giải:

 `19)`

`(x+1)/(x+2):(x+2)/(x+3):(x+3)/(x+1)`

`( đ k : x\ne-2;x\ne-3;x\ne-1)`

`=(x+1)/(x+2).(x+3)/(x+2).(x+1)/(x+3)`

`=((x+1).(x+3).(x+1))/((x+2).(x+2).(x+3))`

`=((x+1)^{2})/((x+2)^{2})`

`=(x^{2}+2.x.1+1^{2})/(x^{2}+2.x.2+2^{2})`

`=(x^{2}+2x+1)/(x^{2}+4x+4)`

`20)(x^{2}+x)/(x+2):(x+3)/(x+2).(x+3)/(x+1)`

`( đ k : x\ne-1;x\ne-2;x\ne-3)`

`=(x.(x+1))/(x+2).(x+2)/(x+3).(x+3)/(x+1)`

`=(x.(x+1).(x+2).(x+3))/((x+2).(x+3).(x+1))`

`=x`

`21)(x+1)/(x+2).((x+2)/(x+3):(x+3)/(x+1))`

`( đ k : x\ne-1;x\ne-2;x\ne-3)`

`=(x+1)/(x+2).(x+2)/(x+3).(x+1)/(x+3)`

`=((x+1).(x+2).(x+1))/((x+2).(x+3).(x+3))`

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

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

`=(x^{2}+2x+1)/(x^{2}+6x+9)`

`22)(x-2)/(x+1).(x^{2}-2x-3)/(x^{2}-5x+6)`

`(đ k : x\ne-1;x\ne2;x\ne3)`

`=((x-2).(x^{2}-3x+x-3))/((x+1).(x^{2}-3x-2x+6))`

`=((x-2).[x.(x-3)+1.(x-3)])/((x+1).[x.(x-3)-2.(x-3)])`

`=((x-2).(x+1).(x-3))/((x+1).(x-2).(x-3))`

`=1`

`23)(x+1)/(x^{2}-2x-8).(4-x)/(x^{2}+x)`

`( đ k : x\ne0;x\ne-1;x\ne4;x\ne-2)`

`=(x+1)/(x^{2}-4x+2x-8).(-(x-4))/(x.(x+1))`

`=((x+1).(-1).(x-4))/([x.(x-4)+2.(x-4)].x.(x+1))`

`=(-(x-4))/((x+2).(x-4).x)`

`=(-1)/(x.(x+2))`

`24)(x^{2}+2)/(4x+24).(x^{2}-36)/(x^{2}+x-2)`

`( đ k : x\ne-6;x\ne1;x\ne-2)`

`=((x^{2}+2).(x^{2}-6^{2}))/(4.(x+6).(x^{2}+x-2))`

`=((x^{2}+2).(x-6).(x+6))/(4.(x+6).(x^{2}+x-2))`

`=((x^{2}+2).(x-6))/(4.(x^{2}+x-2))`

`=(x^{3}-6x^{2}+2x-12)/(4x^{2}+4x-8)`

`25)(x^{3}-8)/(5x+20).(x^{2}+4x)/(x^{2}+2x+4)`

`( đ k : x\ne-4)`

`=((x^{3}-2^{3}).x.(x+4))/(5.(x+4).(x^{2}+2x+4))`

`=((x-2).(x^{2}+x.2+2^{2]).x)/(5.(x^{2}+x.2+2^{2}))`

`=(x.(x-2))/(5)`

`=(x^{2}-2x)/(5)`

`26)((x-3)^{3})/(3x^{2}):(x^{2}-6x+9)/(6x)`

`( đ k : x\ne0;x\ne3)`

`=((x-3)^{3})/(3x^{2]).(6x)/(x^{2}-2.x.3+3^{2})`

`=((x-3)^{3}.3x.2)/(3x.x.(x-3)^{2})`

`=(2.(x-3))/(x)`

`=(2x-6)/(x)`

`27)(x^{2}+x)/(5x^{2}-10x+5):(3x+3)/(5x-5)`

`( đ k : x\ne1;x\ne-1)`

`=(x.(x+1))/(5.(x^{2}-2.x.1+1^{2})).(5.(x-1))/(3.(x+1))`

`=(x.(x+1).5.(x-1))/(5.(x-1)^{2}.(x+1))`

`=(5x)/(5.(x-1))`

`=(x)/(x-1)`