To solve the equation $\frac{1}{x} + 2 = \frac{4}{x} + 4$, let's follow these steps:

Step 1: Subtract $\frac{1}{x}$ from both sides.

$\frac{1}{x} + 2 - \frac{1}{x} = \frac{4}{x} + 4 - \frac{1}{x}$ This simplifies to: $2 = \frac{3}{x} + 4$

Step 2: Subtract 4 from both sides.

$2 - 4 = \frac{3}{x} + 4 - 4$ This simplifies to: $-2 = \frac{3}{x}$

Step 3: Multiply both sides by $x$ to solve for $x$.

$-2x = 3$

Step 4: Divide both sides by -2.

$x = -\frac{3}{2}$

So, the solution is $x = -\frac{3}{2}$.

Would you like more details, or do you have any questions?

Here are 5 related questions you might find helpful:

1. How do you solve equations involving fractions and variables?
2. What are the methods to solve linear equations with variables on both sides?
3. How can you check the solution to an equation?
4. What are common mistakes when solving equations involving fractions?
5. How do you solve equations with more than one variable?

Tip: Always check your solution by substituting it back into the original equation to ensure it satisfies the equation.