Question

1/x-2+2/x-1=6/x where x is not equal to 0,1,2.solve for x

Answer 1

1/x-2+2/x-1=6/x

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

x-1+2x-4/x2-x-2x+2=6/x

3x-5/x2-3x+2=6/x

x(3x-5)=6(x2-3x+2)

3x2-5x=6x2-18x+12

6x2-3x2-18x+5x+12=0

3x2-13x+12=0

3x2-9x-4x+12=0

3x(x-3)-4(x-3)=0

(x-3)(3x-4)=0

x-3=0 3x-4=0

x=3 &x=4/3

Hop

Answer 2

Answer:

Step-by-step explanation:

Solution :-

Here we have,

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

⇒ (x - 2) + 2(x - 2)/(x - 2) (x - 1) = 6/x

⇒ 3x - 5/x² - 3x + 2 = 6/x

⇒ 3x² - 5x = 6x² - 18x + 12

⇒ 3x² - 13x + 12 = 0

By using factorization method, we get

⇒ 3x² - 13x + 12 = 0

⇒ 3x² - 9x - 4x + 12 = 0

⇒ 3x(x - 3) - 4(x - 3) = 0

⇒ (x - 3) (3x - 4) = 0

⇒ x - 3 = 0 or 3x - 4 = 0

⇒ x = 3, 4/3

Here, x = 3, 4/3