If p = 4,q = 3 and r = -2, find the values of :
`(3pq+2qr^(2))/(p+q-r)`

Answer

To solve the expression \((3pq + 2qr^2) / (p + q - r)\) given \(p = 4\), \(q = 3\), and \(r = -2\), we will follow these steps:

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

We start by substituting the values:
- \(p = 4\)
- \(q = 3\)
- \(r = -2\)

So, we have:
\[ \frac{3(4)(3) + 2(3)(-2)^2}{4 + 3 - (-2)} \]

### Step 2: Calculate the numerator.

Now, we will calculate the numerator \(3pq + 2qr^2\):
1. Calculate \(3pq\):
\[ 3(4)(3) = 36 \]
2. Calculate \(2qr^2\):
- First, calculate \(r^2\):
\[ (-2)^2 = 4 \]
- Now substitute into \(2qr^2\):
\[ 2(3)(4) = 24 \]
3. Add both parts together:
\[ 36 + 24 = 60 \]

### Step 3: Calculate the denominator.

Next, we calculate the denominator \(p + q - r\):
\[ 4 + 3 - (-2) = 4 + 3 + 2 = 9 \]

### Step 4: Combine the results.

Now we can combine the results from the numerator and denominator:
\[ \frac{60}{9} \]

### Step 5: Simplify the fraction.

We can simplify \(\frac{60}{9}\) by dividing both the numerator and denominator by their greatest common divisor, which is 3:
\[ \frac{60 \div 3}{9 \div 3} = \frac{20}{3} \]

### Final Answer:
Thus, the final value of the expression is:
\[ \frac{20}{3} \]

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