Answer: The error in the solution is that when multiplying both sides of the equation by x, you didn't take into account that x could be equal to zero. Dividing by zero is undefined, so it's important to check if the solution satisfies this condition.
Explanation:
Here's the correct way to solve the equation:
Starting with the equation:
5/x = x - 4
First, we'll multiply both sides by x to eliminate the fraction:
5 = x^2 - 4x
Now, we have a quadratic equation. To solve it, we'll move all terms to one side and set the equation equal to zero:
x^2 - 4x - 5 = 0
Now, we can factor this quadratic equation:
(x - 5)(x + 1) = 0
To find the values of x, we set each factor equal to zero:
x - 5 = 0
x = 5
x + 1 = 0
x = -1
So, the solutions to the equation are x = 5 and x = -1.
However, remember that we initially had a fraction with 5/x. We must check if x = 0 is a valid solution:
If x = 0:
5/0 is undefined, so x = 0 is not a valid solution.
Therefore, the correct solution to the equation is x = -1.