## Simplifying the Expression (x+1/2)/(2+1/x)

This article will guide you through simplifying the expression **(x+1/2)/(2+1/x)**. We'll break down the steps and explain the rationale behind each one.

### 1. Combining Terms in the Numerator and Denominator

The first step is to combine the terms in both the numerator and denominator. We can do this by finding a common denominator for each fraction:

**Numerator:**(x + 1/2) = (2x/2 + 1/2) = (2x+1)/2**Denominator:**(2 + 1/x) = (2x/x + 1/x) = (2x+1)/x

Now our expression looks like this: **((2x+1)/2) / ((2x+1)/x)**

### 2. Dividing Fractions

Dividing by a fraction is the same as multiplying by its reciprocal. This means we can flip the denominator and multiply:

**((2x+1)/2) * (x/(2x+1))**

### 3. Cancellation and Simplification

Notice that (2x+1) appears in both the numerator and denominator. We can cancel these terms out:

**(1/2) * (x/1)**

Finally, we can simplify to get our final answer:

**x/2**

### Conclusion

Therefore, the simplified expression of **(x+1/2)/(2+1/x)** is **x/2**. Remember, this simplification is only valid for values of x that don't make the original expression undefined (i.e., x cannot be 0 or -1/2).