Evaluate the following limits :
`Lim_(x to 1 ) (x-1)/(x+1)`

Answer

To evaluate the limit \( \lim_{x \to 1} \frac{x-1}{x+1} \), we can follow these steps:

### Step 1: Identify the limit expression
We start with the limit expression:
\[ \lim_{x \to 1} \frac{x-1}{x+1} \]

### Step 2: Substitute the limit value
We can directly substitute \( x = 1 \) into the expression:
\[ \frac{1-1}{1+1} = \frac{0}{2} \]

### Step 3: Simplify the expression
The result of the substitution gives us:
\[ \frac{0}{2} = 0 \]

### Step 4: Conclusion
Thus, the limit evaluates to:
\[ \lim_{x \to 1} \frac{x-1}{x+1} = 0 \]

### Final Answer
The final answer is:
\[ 0 \]