Question

Solve for x: 1/(x-1)(x-2)+1/(x-2)(x-3)=2/3; where x is not equal to 1, 2, 3

Answer 1

x =0,4

Explanation

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

$\frac{(x - 3) + (x - 1)}{(x - 1)(x - 2)(x - 3)} = \frac{2}{3}$

$\frac{2x - 4}{(x - 1)(x - 2)(x - 3)} = \frac{2}{3}$

$\frac{2(x - 2)}{(x - 1)(x - 2)(x - 3)} = \frac{2}{3}$

$\frac{2}{(x - 1)(x - 3)} = \frac{2}{3}$

$\frac{1}{(x - 1)(x - 3)} = \frac{1}{3}$

(x-1)(x-3) = 3

${x}^{2} - 4x + 3 = 3$

${x}^{2} - 4x = 0$

x(x-4)=0

x=0 or x=4

x =0,4

Answer 2

Answer:

x=0 or x=4

x =0,4

Step-by-step explanation: