Question

Solve the equation. $$\frac{1}{4}+\frac{4}{x}=\frac{1}{x}$$

Short answer

The solution to the equation \(\frac{1}{4}+\frac{4}{x}=\frac{1}{x}\) is \(x = -12\).

Step-by-step solution

Eliminate the denominators

To make the equation easier to handle, first multiply every term by \(4x\), which is the least common multiplier. So the given equation \(\frac{1}{4}+\frac{4}{x}=\frac{1}{x}\) would be transformed to \(x+16=4\).

Solve for \(x\)

Rearrange the equation to find the solution for \(x\). It should look like this: \(x=4-16\).

Check the solution

The last step is to check if the solution \(x=-12\) is correct, by substituting \(x\) with \(-12\) in the original equation. You can confirm if \(\frac{1}{4}+\frac{4}{-12}=\frac{1}{-12}\). Checking will find that both sides of the equation are equal. So, \(x = -12\) is the correct solution.