To solve this problem, we need to handle each fraction separately and then combine the results. Let’s break down the problem into clear steps:
Step 1: Solve the first fraction [tex]\(\frac{|-3| \times |4-9|}{\left|-\frac{3}{5} \times 25\right|}\)[/tex]
1. Calculate [tex]\( | -3 | \)[/tex]:
[tex]\[
| -3 | = 3
\][/tex]
2. Calculate [tex]\( | 4 - 9 | \)[/tex]:
[tex]\[
4 - 9 = -5 \quad \text{and} \quad | -5 | = 5
\][/tex]
3. Multiply the absolute values:
[tex]\[
3 \times 5 = 15
\][/tex]
4. Calculate [tex]\( \left| -\frac{3}{5} \times 25 \right| \)[/tex]:
- First, find the product [tex]\( -\frac{3}{5} \times 25 \)[/tex]:
[tex]\[
-\frac{3}{5} \times 25 = -15
\][/tex]
- Then, take the absolute value:
[tex]\[
| -15 | = 15
\][/tex]
5. Form the first fraction:
[tex]\[
\frac{15}{15} = 1
\][/tex]
Step 2: Solve the second fraction [tex]\(\frac{\left|-1-\frac{1}{3}\right|}{-\left|1+\frac{1}{3}\right|}\)[/tex]
1. Calculate [tex]\( \left| -1 - \frac{1}{3} \right| \)[/tex]:
- Convert [tex]\(-\frac{1}{3}\)[/tex] to a fraction and combine terms:
[tex]\[
-1 - \frac{1}{3} = -\frac{3}{3} - \frac{1}{3} = -\frac{4}{3}
\][/tex]
- Then, take the absolute value:
[tex]\[
\left| -\frac{4}{3} \right| = \frac{4}{3}
\][/tex]
2. Calculate [tex]\( -\left| 1 + \frac{1}{3} \right| \)[/tex]:
- Combine terms:
[tex]\[
1 + \frac{1}{3} = \frac{3}{3} + \frac{1}{3} = \frac{4}{3}
\][/tex]
- Take the absolute value:
[tex]\[
\left| \frac{4}{3} \right| = \frac{4}{3}
\][/tex]
- Then negate it:
[tex]\[
-\left| \frac{4}{3} \right| = -\frac{4}{3}
\][/tex]
3. Form the second fraction:
[tex]\[
\frac{\frac{4}{3}}{-\frac{4}{3}} = -1
\][/tex]
Step 3: Combine the results from both fractions:
Combine the results from both steps:
[tex]\[
1 - (-1) = 1 + 1 = 2
\][/tex]
Thus, the final result is:
[tex]\[
\boxed{2}
\][/tex]
So the correct option is [tex]\( \text{H. 2} \)[/tex].
