(15/14-12/25):23/35

To solve the expression \((\frac{15}{14} - \frac{12}{25}) : \frac{23}{35}\), we need to follow the order of operations.

First, we simplify the expression inside the parentheses:

1. Find a common denominator for \(\frac{15}{14}\) and \(\frac{12}{25}\). The least common multiple (LCM) of 14 and 25 is 350.

   • Convert \(\frac{15}{14}\): \[ \frac{15}{14} = \frac{15 \times 25}{14 \times 25} = \frac{375}{350} \]

   • Convert \(\frac{12}{25}\): \[ \frac{12}{25} = \frac{12 \times 14}{25 \times 14} = \frac{168}{350} \]

2. Now, subtract the two fractions: \[ \frac{375}{350} - \frac{168}{350} = \frac{375 - 168}{350} = \frac{207}{350} \]

Next, we need to divide \(\frac{207}{350}\) by \(\frac{23}{35}\):

3. Instead of dividing, multiply by the reciprocal: \[ \frac{207}{350} \div \frac{23}{35} = \frac{207}{350} \times \frac{35}{23} \]

4. Multiply the fractions: \[ = \frac{207 \times 35}{350 \times 23} \]

Next, we can simplify:

• The \(35\) in the numerator and \(350\) in the denominator can be simplified: \[ 350 = 10 \times 35 \quad \text{so,} \quad \frac{35}{350} = \frac{1}{10} \]

Thus, we have: \[ \frac{207 \times 1}{10 \times 23} = \frac{207}{230} \]

5. Final result: The simplified result of the expression \((\frac{15}{14} - \frac{12}{25}) : \frac{23}{35}\) is: \[ \frac{207}{230} \]