`'*'` on `Q` defined by `a*b=(a-1)/(b+1)` for all `a ,\ b in Q` define a binary operation on the given set or not:

Explanation

To determine whether the operation defined by \( a * b = \frac{a - 1}{b + 1} \) for all \( a, b \in \mathbb{Q} \) is a binary operation on the set of rational numbers \( \mathbb{Q} \), we need to check if it satisfies the closure property.

### Step-by-Step Solution:

1. **Understanding Closure Property**:
A binary operation on a set is said to be closed if, for any two elements \( a \) and \( b \) in the set, the result of the operation \( a * b \) is also in the set.

2. **Define the Operation**:
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