Question

1/(x-1)(x-2) +1/(x-2)(x-3) +1/(x-3)(x-4)=1/6 factorise​

Answer 1

こんにちは、私は科学グループに興味があります。

Answer 2

1/(x - 1)(x - 2) +1/(x - 2)(x - 3) +1/(x - 3)(x - 4)=1/6

[1/(x - 1)(x - 2) +1/(x - 2)(x - 3)] + 1/(x - 3)(x - 4) = 1/6

[(x - 3)+(x - 1)/(x - 1)(x - 2)(x - 3)] + 1/(x - 3)(x - 4) = 1/6

[(2x - 4)/(x-  1)(x - 2)(x - 3)] + 1/(x - 3)(x - 4) = 1/6

[2(x - 2)/(x - 1)(x - 2)(x - 3)] + 1/(x - 3)(x - 4) = 1/6

2/(x - 1)(x - 3) +  1/(x - 3)(x - 4) = 1/6

[2(x - 4) + (x - 1)]/(x - 3)(x - 4)(x - 1) = 1/6

[2x - 8 + x - 1]/(x - 3)(x - 4)(x - 1) = 1/6

(3x - 9)/(x - 3)(x - 4)(x - 1) = 1/6

3(x- 3)/(x - 3)(x - 4)(x - 1) = 1/6

3/(x - 4)(x - 1) = 1/6

3 × 6 = (x - 4)(x - 1)

18 = x² - x - 4x + 4

x² - 5x - 14 = 0

x² -7x + 2x - 14 = 0

x(x - 7) + 2(x - 7) = 0

(x + 2)(x - 7) = 0

x = - 2    or x = 7