Answer: 4
Step-by-step explanation: To solve the equation (x/(x-2)) + (1/5) = (2/(x-2)), we can follow these steps:
Step 1: Find a common denominator for the fractions on the left-hand side of the equation. The common denominator will be (5(x-2)).
Step 2: Rewrite the equation using the common denominator:
[(5(x)/(x-2)) + (1(x-2))/(5(x-2))] = (2/(x-2))
Step 3: Simplify the equation:
(5x + (x - 2))/(5(x-2)) = (2/(x-2))
Step 4: Combine like terms:
(6x - 2)/(5(x-2)) = (2/(x-2))
Step 5: Cross-multiply to eliminate the denominators:
(6x - 2)(x-2) = 2 * 5(x-2)
Step 6: Expand and simplify both sides of the equation:
6x^2 - 20x + 4 = 10x - 20
Step 7: Rearrange the equation to one side:
6x^2 - 30x + 24 = 0
Step 8: Divide the equation by 6 to simplify:
x^2 - 5x + 4 = 0
Step 9: Factor the quadratic equation:
(x - 4)(x - 1) = 0
Step 10: Solve for x:
x - 4 = 0 or x - 1 = 0
x = 4 or x = 1
Therefore, the solutions for x are 4 and 1.