Đáp án:
`A=(x+4)/(x+2)`
Giải thích các bước giải:
Phân tích:
`+)`
`x^3+8x^2+19x+12`
`=x^3+7x^2+x^2+19x+12`
`=(x^3+x^2)+(7x^2+19x+12)`
`=x^2(x+1)+(7x^2+7x+12x+12)`
`=x^2(x+1)+[(7x^2+7x)+(12x+12)]`
`=x^2(x+1)+[7x(x+1)+12(x+1)]`
`=x^2(x+1)+(x+1)(7x+12)`
`=(x+1)(x^2+7x+12)`
`=(x+1)(x^2+3x+4x+12)`
`=(x+1)[(x^2+3x)+(4x+12)]`
`=(x+1)[x(x+3)+4(x+3)]`
`=(x+1)(x+4)(x+3)(1)`
`+)`
`x^3+6x^2+11x+6`
`=x^3+x^2+5x^2+11x+6`
`=(x^3+x^2)+(5x^2+11x+6)`
`=x^2(x+1)+(5x^2+5x+6x+6)`
`=x^2(x+1)+[(5x^2+5x)+(6x+6)]`
`=x^2(x+1)+[5x(x+1)+6(x+1)]`
`=x^2(x+1)+(5x+6)(x+1)`
`=(x+1)(x^2+5x+6)`
`=(x+1)(x^2+2x+3x+6)`
`=(x+1)[(x^2+2x)+(3x+6)]`
`=(x+1)[x(x+2)+3(x+2)]`
`=(x+1)(x+2)(x+3)(2)`
Từ `(1)` và `(2)`:
`A=(x^3+8x^2+19x+12)/(x^3+6x^2+11x+6)=((x+1)(x+4)(x+3))/((x+1)(x+2)(x+3))=(x+4)/(x+2)`
Vậy `A=(x+4)/(x+2)`
