The value of `(1+1/2)/(1-1/2)div4/7(2/5+3/10)` of `(1/2+1/3)/(1/2-1/3)` is

Options

A. `2/3`
B. `3/2`
C. `18(3)/8`
D. `37(1)/2`

Answer

To solve the expression \((1 + \frac{1}{2}) / (1 - \frac{1}{2}) \div 4 / 7 \left(\frac{2}{5} + \frac{3}{10}\right)\), we will follow the order of operations (BODMAS/BIDMAS). Let's break it down step by step.

### Step 1: Solve the brackets
First, we solve the expression inside the brackets:
1. \(\frac{2}{5} + \frac{3}{10}\)

To add these fractions, we need a common denominator. The least common multiple of 5 and 10 is 10.

\[ \frac{2}{5} = \frac{2 \times 2}{5 \times 2} = \frac{4}{10} \]

Now we can add:
\[ \frac{4}{10} + \frac{3}{10} = \frac{4 + 3}{10} = \frac{7}{10} \]

### Step 2: Solve the first part of the expression
Next, we solve the first part of the expression:
\[ (1 + \frac{1}{2}) / (1 - \frac{1}{2}) \]

Calculating the numerator:
\[ 1 + \frac{1}{2} = \frac{2}{2} + \frac{1}{2} = \frac{3}{2} \]

Calculating the denominator:
\[ 1 - \frac{1}{2} = \frac{2}{2} - \frac{1}{2} = \frac{1}{2} \]

Now we can divide:
\[ \frac{3/2}{1/2} = \frac{3}{2} \times \frac{2}{1} = 3 \]

### Step 3: Combine the results
Now we have:
\[ 3 \div 4 \div 7 \times \frac{7}{10} \]

### Step 4: Solve the division and multiplication
First, we handle the division:
\[ 3 \div 4 = \frac{3}{4} \]

Next, we divide by 7:
\[ \frac{3/4}{7} = \frac{3}{4} \times \frac{1}{7} = \frac{3}{28} \]

Now we multiply by \(\frac{7}{10}\):
\[ \frac{3}{28} \times \frac{7}{10} = \frac{3 \times 7}{28 \times 10} = \frac{21}{280} \]

### Step 5: Simplify the fraction
To simplify \(\frac{21}{280}\), we find the greatest common divisor (GCD) of 21 and 280, which is 7:
\[ \frac{21 \div 7}{280 \div 7} = \frac{3}{40} \]

### Final Answer
The value of the expression is \(\frac{3}{40}\).

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