If p = 3 , q = 2 and r = -1, find the values of
`(3p^(2)q+5r)/(2pq-3qr)`

Answer

To solve the expression \((3p^{2}q + 5r)/(2pq - 3qr)\) given \(p = 3\), \(q = 2\), and \(r = -1\), we will follow these steps:

### Step 1: Substitute the values of \(p\), \(q\), and \(r\) into the expression.

We start with the expression:
\[ \frac{3p^{2}q + 5r}{2pq - 3qr} \]

Substituting \(p = 3\), \(q = 2\), and \(r = -1\):
\[ \frac{3(3)^{2}(2) + 5(-1)}{2(3)(2) - 3(2)(-1)} \]

### Step 2: Calculate \(p^2\) and substitute it into the expression.

Calculating \(p^2\):
\[ p^2 = 3^2 = 9 \]
Now substituting \(p^2\) into the expression:
\[ \frac{3(9)(2) + 5(-1)}{2(3)(2) - 3(2)(-1)} \]

### Step 3: Simplify the numerator.

Calculating the numerator:
\[ 3(9)(2) = 54 \]
\[ 5(-1) = -5 \]
So the numerator becomes:
\[ 54 - 5 = 49 \]

### Step 4: Simplify the denominator.

Calculating the denominator:
\[ 2(3)(2) = 12 \]
\[ 3(2)(-1) = -6 \quad \text{(since } -3 \times 2 \times -1 = 6\text{)} \]
So the denominator becomes:
\[ 12 + 6 = 18 \]

### Step 5: Combine the results.

Now we have:
\[ \frac{49}{18} \]

### Step 6: Convert to decimal (if needed).

To convert \(\frac{49}{18}\) to decimal:
\[ 49 \div 18 \approx 2.72 \]

Thus, the final value of the expression is:
\[ \frac{49}{18} \text{ or approximately } 2.72 \]

### Final Answer:
\[ \frac{49}{18} \text{ or } 2.72 \]

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