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

Answer

To solve the expression \((p^{2}+q^{2}-r^{2})/(pq+qr-pr)\) 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.

The expression is:
\[ \frac{p^{2}+q^{2}-r^{2}}{pq+qr-pr} \]

Substituting the values:
\[ \frac{4^{2}+3^{2}-(-2)^{2}}{4 \cdot 3 + 3 \cdot (-2) - 4 \cdot (-2)} \]

### Step 2: Calculate the squares in the numerator.

Calculating \(4^{2}\), \(3^{2}\), and \((-2)^{2}\):
\[ 4^{2} = 16, \quad 3^{2} = 9, \quad (-2)^{2} = 4 \]

Now substitute these values into the numerator:
\[ 16 + 9 - 4 \]

### Step 3: Simplify the numerator.

Calculating the numerator:
\[ 16 + 9 = 25 \]
\[ 25 - 4 = 21 \]

So, the numerator is \(21\).

### Step 4: Calculate the terms in the denominator.

Calculating \(pq\), \(qr\), and \(-pr\):
\[ pq = 4 \cdot 3 = 12 \]
\[ qr = 3 \cdot (-2) = -6 \]
\[ -pr = -4 \cdot (-2) = 8 \]

Now substitute these values into the denominator:
\[ 12 + (-6) + 8 \]

### Step 5: Simplify the denominator.

Calculating the denominator:
\[ 12 - 6 = 6 \]
\[ 6 + 8 = 14 \]

So, the denominator is \(14\).

### Step 6: Combine the results.

Now we can combine the results from the numerator and denominator:
\[ \frac{21}{14} \]

### Step 7: Simplify the fraction.

We can simplify \(\frac{21}{14}\) by dividing both the numerator and denominator by their greatest common divisor (GCD), which is \(7\):
\[ \frac{21 \div 7}{14 \div 7} = \frac{3}{2} \]

### Final Answer:
The value of the expression is \(\frac{3}{2}\).

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