The relation `p/((p + 1)) > 1` is valid when :

Options

A. `p ge -1`
B. `p gt -1`
C. `p lt - 1`
D. `-1 lt p lt 0`

Answer

To solve the inequality \( \frac{p}{p + 1} > 1 \), we will follow these steps:

### Step 1: Rewrite the inequality
Start by rewriting the inequality:
\[ \frac{p}{p + 1} > 1 \]

### Step 2: Move all terms to one side
Subtract 1 from both sides:
\[ \frac{p}{p + 1} - 1 > 0 \]

### Step 3: Combine the fractions
To combine the fractions, we need a common denominator:
\[ \frac{p - (p + 1)}{p + 1} > 0 \]
This simplifies to:
\[ \frac{p - p - 1}{p + 1} > 0 \]
Which further simplifies to:
\[ \frac{-1}{p + 1} > 0 \]

### Step 4: Analyze the inequality
The fraction \(\frac{-1}{p + 1}\) is greater than 0 when the denominator \(p + 1\) is negative (since the numerator is negative). Therefore, we need:
\[ p + 1 < 0 \]

### Step 5: Solve for \(p\)
Solving the inequality:
\[ p < -1 \]

### Conclusion
The relation \( \frac{p}{p + 1} > 1 \) is valid when \( p < -1 \).