To solve the equation, we need to eliminate the denominators by multiplying both sides of the equation by the LCD (Least Common Denominator) of the fractions, which is x(x-2):
8/x * x(x-2) = 6/x-2 * x(x-2)
8(x-2) = 6x
8x - 16 = 6x
Subtracting 6x from both sides:
2x - 16 = 0
Adding 16 to both sides:
2x = 16
Dividing both sides by 2:
x = 8
Therefore, the solution to the equation is x = 8.
To check the solution, we substitute x = 8 back into the original equation:
8/x = 6/x-2
8/8 = 6/8-2
1 = 6/6
1 = 1
Since the original equation holds true when x = 8, we can confirm that x = 8 is indeed the correct solution.
The correct answer is option C. X = 8.
Solve the equation. Check your solution.
6. 8/x = 6/x-2
A. x=-1/8
B. No solution
C. X = 8
D. X = -8
1 answer
1 answer