Rút gọn và tính

Let's simplify and calculate each of the expressions step by step.

### 1)
\[
\left( \frac{-25}{27} \frac{31}{42} \right) - \left( \frac{-7}{27} \frac{3}{42} \right)
\]

First, we need to multiply the fractions:

1. \(\frac{-25}{27} \times \frac{31}{42} = \frac{-775}{1134}\)
2. \(\frac{-7}{27} \times \frac{3}{42} = \frac{-21}{1134}\)

Now, we combine the two results:
\[
\frac{-775}{1134} - \frac{-21}{1134} = \frac{-775 + 21}{1134} = \frac{-754}{1134}
\]

Now simplify:
\[
\frac{-754}{1134} = \frac{-377}{567} \quad (\text{dividing both by 2})
\]

### 2)
\[
\left( \frac{-13}{25} \times \frac{5}{32} \right) - \left( \frac{-13}{25} \times (-64) \right)
\]

Calculating each term:
1. \(\frac{-13}{25} \times \frac{5}{32} = \frac{-65}{800}\)
2. \(\frac{-13}{25} \times (-64) = \frac{832}{25}\)

Finding a common denominator (which can be \(800\)):
1. \(\frac{832 \times 32}{25 \times 32} = \frac{26624}{800}\)

Combining:
\[
\frac{-65}{800} + \frac{26624}{800} = \frac{26624 - 65}{800} = \frac{26559}{800}
\]

### 3)
\[
\frac{3}{8} - \frac{23}{14} - \frac{3}{8} - \frac{9}{14}
\]

Finding the common denominator which is \(56\):
1. \(\frac{3}{8} = \frac{21}{56}\)
2. \(\frac{-23}{14} = \frac{-92}{56}\)
3. \(\frac{3}{8} = \frac{21}{56}\)
4. \(\frac{-9}{14} = \frac{-36}{56}\)

Combining:
\[
\frac{21 - 92 + 21 - 36}{56} = \frac{-86}{56} = \frac{-43}{28}
\]

### 4)
\[
\frac{5}{12} + \frac{4}{5} - \frac{3}{4} + \frac{1}{4}
\]

Convert to a common denominator. The LCM of \(12, 5, 4\) is \(60\):
1. \(\frac{5}{12} = \frac{25}{60}\)
2. \(\frac{4}{5} = \frac{48}{60}\)
3. \(\frac{3}{4} = \frac{45}{60}\)
4. \(\frac{1}{4} = \frac{15}{60}\)

Now combine:
\[
\frac{25 + 48 - 45 + 15}{60} = \frac{43}{60}
\]

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### Final Results:

1) \(\frac{-377}{567}\)

2) \(\frac{26559}{800}\)

3) \(\frac{-43}{28}\)

4) \(\frac{43}{60}\)