To solve the expression

\[
\left( \frac{3}{4} - \frac{3}{7} \right) - \left( \frac{9}{13} - \frac{3}{7} \right) - \left( -\frac{1}{4} - \frac{9}{13} \right),
\]

we break it down into three parts.

### Step 1: Calculate \(\frac{3}{4} - \frac{3}{7}\)

First, we find a common denominator for \(\frac{3}{4}\) and \(\frac{3}{7}\). The least common multiple of \(4\) and \(7\) is \(28\).

Convert each fraction:

\[
\frac{3}{4} = \frac{3 \times 7}{4 \times 7} = \frac{21}{28},
\]
\[
\frac{3}{7} = \frac{3 \times 4}{7 \times 4} = \frac{12}{28}.
\]

Now, we subtract:

\[
\frac{21}{28} - \frac{12}{28} = \frac{21 - 12}{28} = \frac{9}{28}.
\]

### Step 2: Calculate \(\frac{9}{13} - \frac{3}{7}\)

Next, we find a common denominator for \(\frac{9}{13}\) and \(\frac{3}{7}\). The least common multiple of \(13\) and \(7\) is \(91\).

Convert each fraction:

\[
\frac{9}{13} = \frac{9 \times 7}{13 \times 7} = \frac{63}{91},
\]
\[
\frac{3}{7} = \frac{3 \times 13}{7 \times 13} = \frac{39}{91}.
\]

Now, we subtract:

\[
\frac{63}{91} - \frac{39}{91} = \frac{63 - 39}{91} = \frac{24}{91}.
\]

### Step 3: Calculate \(-\frac{1}{4} - \frac{9}{13}\)

Finding a common denominator for \(-\frac{1}{4}\) and \(\frac{9}{13}\), we find the least common multiple of \(4\) and \(13\) is \(52\).

Convert each fraction:

\[
-\frac{1}{4} = -\frac{1 \times 13}{4 \times 13} = -\frac{13}{52},
\]
\[
\frac{9}{13} = \frac{9 \times 4}{13 \times 4} = \frac{36}{52}.
\]

Now, we subtract:

\[
-\frac{13}{52} - \frac{36}{52} = -\frac{13 + 36}{52} = -\frac{49}{52}.
\]

### Step 4: Combine the results

Now, we have:

\[
\frac{9}{28} - \frac{24}{91} - \left(-\frac{49}{52}\right) = \frac{9}{28} - \frac{24}{91} + \frac{49}{52}.
\]

To combine these fractions, we find the least common multiple of \(28\), \(91\), and \(52\). The LCM is \(1092\).

Convert each fraction:

For \(\frac{9}{28}\):

\[
\frac{9}{28} = \frac{9 \times 39}{28 \times 39} = \frac{351}{1092}.
\]

For \(-\frac{24}{91}\):

\[
-\frac{24}{91} = \frac{-24 \times 12}{91 \times 12} = -\frac{288}{1092}.
\]

For \(\frac{49}{52}\):

\[
\frac{49}{52} = \frac{49 \times 21}{52 \times 21} = \frac{1029}{1092}.
\]

Now, combine these:

\[
\frac{351}{1092} - \frac{288}{1092} + \frac{1029}{1092} = \frac{351 - 288 + 1029}{1092} = \frac{1092}{1092} = 1.
\]

Thus, the final result is

\[
\boxed{1}.
\]