Tính`1/(x^2+7x+10)+1/(x^2+13x+40)+1/(x^2+19x+88)`

`1/(x^2 + 7x + 10) + 1/(x^2 + 13x + 40) + 1/(x^2 + 19x + 88)`

`= 1/(x^2 + 5x + 2x + 10) + 1/(x^2 + 8x + 5x + 40) + 1/(x^2 + 11x + 8x + 88)`

`= 1/(x(x + 5) + 2(x + 5)) + 1/(x(x + 8) + 5(x + 8)) + 1/(x(x + 11) + 8(x + 11))`

`= 1/((x + 5)(x + 2)) + 1/((x + 8)(x + 5)) + 1/((x + 11)(x + 8))`

`= ((x+8)(x+11))/((x+11)(x + 8)(x + 5)(x + 2)) + ((x+2)(x+11))/((x+11)(x + 8)(x + 5)(x+2)) + ((x+2)(x+5))/((x + 11)(x + 8)(x+5)(x+2))`

`= ((x+8)(x+11)+(x+2)(x+11)+(x+2)(x+5))/((x+11)(x + 8)(x + 5)(x + 2))`

`= (x^2+11x+8x+88+x^2+11x+2x+22+x^2+5x+2x+10)/((x+11)(x + 8)(x + 5)(x + 2))`

`= (3x^2+39x+120)/((x+11)(x + 8)(x + 5)(x + 2))`

`= (3(x^2+13x+40))/((x+11)(x + 8)(x + 5)(x + 2))`

`= (3(x^2+8x+5x+40))/((x+11)(x + 8)(x + 5)(x + 2))`

`= (3(x(x+8)+5(x+8)))/((x+11)(x + 8)(x + 5)(x + 2))`

`= (3(x+8)(x+5))/((x+11)(x + 8)(x + 5)(x + 2))`

`= 3/((x+11)(x + 2))`

Vậy: `1/(x^2 + 7x + 10) + 1/(x^2 + 13x + 40) + 1/(x^2 + 19x + 88) = 3/((x+11)(x + 2))`