Question

Solve for x

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


Where x is not equal to 0,1,2​

Answer 1

Answer:

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

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Answer 2

X = 3,4/3
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