To solve this rational equation, let's begin by getting rid of the denominators. We can do this by multiplying every term in the equation by the least common denominator (LCD), which in this case is x(x - 2)(x - 6).
The original equation is:
2/(x - 6) - 6/(x - 2) = 8/(x^2 - 8x + 12)
The LCD is x(x - 2)(x - 6), so we will multiply each term by this expression:
x(x - 2)(x - 6) * (2/(x - 6)) - x(x - 2)(x - 6) * (6/(x - 2)) = x(x - 2)(x - 6) * (8/(x^2 - 8x + 12))
After multiplying, we get:
2x(x - 2)(x - 6) - 6x(x - 2)(x - 6) = 8x(x - 2)(x - 6)
Now let's simplify:
2x(x - 2)(x - 6) - 6x(x - 2)(x - 6) = 8x(x - 2)(x - 6)
We can see that the terms x - 2 and x - 6 appear on both sides of the equation. We can cancel out these common factors:
2x - 12x = 8x
-10x = 8x
Combining like terms:
-10x - 8x = 0
-18x = 0
Dividing both sides by -18:
x = 0
So the solution to the rational equation is x = 0.
Solve the rational equation. If the equation has no solution, so state.
2/x-6 - 6/x-2 = 8/x^2 - 8x + 12
3 answers
clearly, x=0 does not solve the equation.
The only possible solution of x=6 is not allowed.
So, there is no solution.
The only possible solution of x=6 is not allowed.
So, there is no solution.
Apologies for the earlier mistake. You are correct. After re-evaluating the equation, we find that x = 0 is not a valid solution since it would result in division by zero. Additionally, x = 6 would also make the denominator zero. Therefore, there is no solution to the rational equation. Thank you for catching the error.
1 answer