Question

2/(x-3) + 1/(x-1)= 5/( x-1)-2/(x-2)

Answer 1

Answer:

x = 1, 7/3

Step-by-step explanation:

2 (x - 1) + 1 (x-3) / (x-3) (x-1) = 5 (x-2) - 2 (x-1) / (x-1) (x-2)  (Taking LCM)

2 x - 2 + x -3 / x² -x -3 x + 3 = 5 x - 10 - 2 x +2 / x² - 2 x - x + 2

3 x - 5 / x² - 4 x + 3 = 3 x - 8 / x² - 3 x + 2

(3 x - 5) (x² - 3 x +2) = (3 x - 8) (x² - 4 x + 3)  (Cross Multiplication)

3 x³ - 9 x² + 6 x - 5 x² + 15 x - 10 = 3 x³ - 12 x² + 9 x - 8 x² + 32 x - 24

- 14 x² + 21 x - 10 =  - 20 x² + 41 x - 24

- 14 x² + 21 x - 10 + 20 x² - 41 x + 24 = 0

+ 6 x² - 20 x + 14 = 0

3 x² - 10 x + 7 = 0

3 x² - 7 x - 3 x + 7 = 0

x (3 x - 7) - 1 (3 x - 7) = 0

(x - 1) (3 x - 7) = 0

∴ x = 1, 7/3