If `(p+4)/(p-4)=13`, what is the value of p?

Options

A. `(2)/(3)`
B. `(10)/(13)`
C. `(28)/(9)`
D. `(14)/(3)`

Answer

To solve the equation \(\frac{p+4}{p-4} = 13\), we will follow these steps:

### Step 1: Cross-Multiply
We start by cross-multiplying to eliminate the fraction:
\[ p + 4 = 13(p - 4) \]

### Step 2: Distribute on the Right Side
Now, we distribute \(13\) on the right side:
\[ p + 4 = 13p - 52 \]

### Step 3: Rearrange the Equation
Next, we rearrange the equation to get all terms involving \(p\) on one side and constant terms on the other side:
\[ p - 13p = -52 - 4 \]
This simplifies to:
\[ -12p = -56 \]

### Step 4: Solve for \(p\)
Now, we divide both sides by \(-12\) to solve for \(p\):
\[ p = \frac{-56}{-12} = \frac{56}{12} \]

### Step 5: Simplify the Fraction
Finally, we simplify the fraction:
\[ p = \frac{56 \div 4}{12 \div 4} = \frac{14}{3} \]

Thus, the value of \(p\) is \(\frac{14}{3}\).

### Final Answer:
The value of \(p\) is \(\frac{14}{3}\).

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