3/x - 1 + 1/x - 3 = 4/x - 2. Find x.

The solution is obtained by simplifying the algebraic expression.

Answer: The solution of 3/x-1+1/x-3=4/x-2 is x = 4.

Let's find x.

Explanation:

3/x-1 + 1/x-3 = 4/x-2

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

⇒ [ 3x - 9 + x -1 ] / [ (x-1)(x-3) ] = 4 / x-2 ---------------> Taking LCM

⇒ [ 4x - 10 ] / [ (x-1)(x-3) ] = 4 / x-2

⇒ (4x -10) (x - 2) = 4 (x -1)(x-3)      --------------> cross multiplication

⇒ 4x² - 18x + 20 = 4x² - 16x + 12  ---------------> cancel the terms 4x² on both sides

⇒ -18x + 20 = -16x + 12

⇒ -18x + 16x = -20 + 12

⇒ - 2x = - 8

⇒ x = 4

Thus, the solution of 3/x-1+1/x-3=4/x-2 is x = 4.