Simplify : `(2//7+3//5)div(2//5+2//7)`
A. `31//24`
B. `24//31`
C. `26//25`
D. `12//13`

Options

A. C
B. D
C. B
D. A

Answer

To simplify the expression \((\frac{2}{7} + \frac{3}{5}) \div (\frac{2}{5} + \frac{2}{7})\), we will follow these steps:

### Step 1: Simplify the Numerator
First, we need to simplify the numerator \(\frac{2}{7} + \frac{3}{5}\).

To add these fractions, we need a common denominator. The least common multiple (LCM) of 7 and 5 is 35.

\[ \frac{2}{7} = \frac{2 \times 5}{7 \times 5} = \frac{10}{35} \]
\[ \frac{3}{5} = \frac{3 \times 7}{5 \times 7} = \frac{21}{35} \]

Now, we can add them:
\[ \frac{2}{7} + \frac{3}{5} = \frac{10}{35} + \frac{21}{35} = \frac{31}{35} \]

### Step 2: Simplify the Denominator
Next, we simplify the denominator \(\frac{2}{5} + \frac{2}{7}\).

Again, we will use the common denominator of 35.

\[ \frac{2}{5} = \frac{2 \times 7}{5 \times 7} = \frac{14}{35} \]
\[ \frac{2}{7} = \frac{2 \times 5}{7 \times 5} = \frac{10}{35} \]

Now, we can add them:
\[ \frac{2}{5} + \frac{2}{7} = \frac{14}{35} + \frac{10}{35} = \frac{24}{35} \]

### Step 3: Divide the Numerator by the Denominator
Now we have:
\[ \frac{31}{35} \div \frac{24}{35} \]

Dividing by a fraction is the same as multiplying by its reciprocal:
\[ \frac{31}{35} \times \frac{35}{24} = \frac{31 \times 35}{35 \times 24} \]

The \(35\) cancels out:
\[ = \frac{31}{24} \]

### Step 4: Final Answer
Thus, the simplified expression is:
\[ \frac{31}{24} \]