Question

Solve the equation. $$\frac{1}{5}-\frac{2}{5 x}=\frac{1}{x}$$

Short answer

The solution to the equation is \(x = 7\).

Step-by-step solution

Clear the fractions

To get rid of fractions, find the least common multiple (LCM) of the denominators and multiply each term of the equation with it. The LCM of 5, \(5x\), and \(x\) is \(5x\). Then the equation becomes: \(x - 2 = 5\)

Simplify and isolate the variable

Simplify the equation by getting the terms with \(x\) on one side and the constants on the other. Doing it, you get \(x = 2 + 5\)

Solve for the variable

This gives the final answer as \(x = 7\)