To add these fractions, you'll first need to find a common denominator:

1. For \( \frac{3}{5} \) and \( \frac{-9}{10} \), the common denominator is 10.
2. For \( \frac{7}{6} \), the common denominator is 6.

So, let's rewrite these fractions with a common denominator:

1. \( \frac{3}{5} \) becomes \( \frac{6}{10} \)
2. \( \frac{-9}{10} \) remains the same.
3. \( \frac{7}{6} \) becomes \( \frac{35}{30} \)

Now, add them up:

\[ \frac{6}{10} + \frac{-9}{10} - \frac{35}{30} \]

\[ \frac{6 - 9 - 35}{10} \]

\[ \frac{-38}{10} \]

Now, you can simplify this fraction. Divide both the numerator and denominator by their greatest common divisor, which is 2:

\[ \frac{-19}{5} \]

So, \( \frac{3}{5} + \frac{-9}{10} - \frac{7}{6} = \frac{-19}{5} \)

To solve this expression, we follow the order of operations (PEMDAS/BODMAS). 

First, we perform the division within each fraction, then multiply the resulting fractions together.

\[
\frac{1}{20938494839} \times \frac{10293}{109237393}
\]

Let's compute each part separately:

\[
\frac{1}{20938494839} \approx 4.773 \times 10^{-11}
\]

\[
\frac{10293}{109237393} \approx 9.420 \times 10^{-5}
\]

Now, we multiply these two results together:

\[
(4.773 \times 10^{-11}) \times (9.420 \times 10^{-5}) = 4.497 \times 10^{-15}
\]

So, \( \frac{1}{20938494839} \times \frac{10293}{109237393} \) is approximately \(4.497 \times 10^{-15}\).

Hay... >:)

e

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