If m=2, n=3, p=4, q=0,r= 7 and s = 10, then the expression `(3m+2n)/(q+p)-(4p-3n)/(q+r)+(2p+3m)/(q+m)` has the value

Options

A. 5
B. 9
C. 11
D. 13

Answer

To solve the expression \((3m + 2n)/(q + p) - (4p - 3n)/(q + r) + (2p + 3m)/(q + m)\) given the values \(m = 2\), \(n = 3\), \(p = 4\), \(q = 0\), \(r = 7\), and \(s = 10\), we will follow these steps:

### Step 1: Substitute the values into the expression
We start by substituting the values of \(m\), \(n\), \(p\), \(q\), and \(r\) into the expression.

\[ \frac{3(2) + 2(3)}{0 + 4} - \frac{4(4) - 3(3)}{0 + 7} + \frac{2(4) + 3(2)}{0 + 2} \]

### Step 2: Simplify each term
Now we simplify each term in the expression.

1. For the first term:
\[ \frac{3(2) + 2(3)}{4} = \frac{6 + 6}{4} = \frac{12}{4} = 3 \]

2. For the second term:
\[ \frac{4(4) - 3(3)}{7} = \frac{16 - 9}{7} = \frac{7}{7} = 1 \]

3. For the third term:
\[ \frac{2(4) + 3(2)}{2} = \frac{8 + 6}{2} = \frac{14}{2} = 7 \]

### Step 3: Combine the results
Now we combine the results of the simplified terms:
\[ 3 - 1 + 7 \]

### Step 4: Calculate the final result
Calculating the final result:
\[ 3 - 1 = 2 \]
\[ 2 + 7 = 9 \]

### Final Answer
The value of the expression is \(9\).

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