Đáp án:
Ta có :
`1/(x + 2) + 3/(x^2 - 4) + (x - 14)/[(x^2 + 4x + 4).(x - 2)]`
`= 1/(x + 2) + 3/[(x + 2)(x - 2)] + (x - 14)/[(x + 2)^2(x - 2)]`
`= [(x + 2)(x - 2)]/[(x + 2)^2(x - 2)] + [3(x + 2)]/[(x + 2)^2(x - 2)] + (x - 14)/[(x + 2)^2(x - 2)]`
`= [(x + 2)(x - 2) + 3(x + 2) + (x - 14)]/[(x + 2)^2(x - 2)]`
`= (x^2 - 4 + 3x + 6 + x - 14)/[(x + 2)^2(x - 2)] `
`= (x^2 + 4x - 12)/[(x + 2)^2(x - 2)] `
`= [(x^2 - 2x) + (6x - 12)]/[(x + 2)^2(x - 2)] `
`= [x(x - 2) + 6(x - 2)]/[(x + 2)^2(x - 2)] `
`= [(x+ 6)(x - 2)]/[(x + 2)^2(x - 2)] `
`= (x + 6)/(x + 2)^2`
Giải thích các bước giải: