Solve:
`(x-3)/(x+4)gt0,x in R`

Explanation

To solve the inequality \(\frac{x-3}{x+4} > 0\), we will analyze the expression step by step.

### Step 1: Identify the critical points
The critical points occur when the numerator and denominator are equal to zero.

1. **Numerator**: \(x - 3 = 0 \Rightarrow x = 3\)
2. **Denominator**: \(x + 4 = 0 \Rightarrow x = -4\)

### Step 2: Determine intervals
The critical points divide the real number line into intervals. The intervals are:
1. \( (-\infty, -4) \)
2. \( (-4, 3) \)
3. \( (3, \infty) \)

### Step 3: Test each interval
We will test a point from each interval to determine where the inequality holds.

1. **Interval \( (-\infty, -4) \)**: Choose \(x = -5\)
\[ \frac{-5-3}{-5+4} = \frac{-8}{-1} = 8 > 0 \quad \text{(True)} \]

2. **Interval \( (-4, 3) \)**: Choose \(x = 0\)
\[ \frac{0-3}{0+4} = \frac{-3}{4} = -\frac{3}{4} < 0 \quad \text{(False)} \]

3. **Interval \( (3, \infty) \)**: Choose \(x = 4\)
\[ \frac{4-3}{4+4} = \frac{1}{8} > 0 \quad \text{(True)} \]

### Step 4: Combine the results
From the tests, we find that the inequality \(\frac{x-3}{x+4} > 0\) holds true in the intervals:
- \( (-\infty, -4) \)
- \( (3, \infty) \)

### Step 5: Write the solution
The solution to the inequality is:
\[ x \in (-\infty, -4) \cup (3, \infty) \]