6. $$ 3 \frac{3}{4}+2 \frac{1}{3}-1 \frac{5}{12} $$ $$ \frac{3 \frac{3}{4}+2 \frac{1}{2}-1 \frac{5}{12}}{\frac{15}{4}+\frac{7}{3}+\frac{17}{12}} $$ $$ =\frac{12}{12}+1 $$

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Let's solve the expression step by step.

### Step 1: Convert Mixed Numbers to Improper Fractions

1. **Convert $$3 \frac{3}{4}$$**:
   $$
   3 \frac{3}{4} = 3 \times 4 + 3 = 12 + 3 = \frac{15}{4}
   $$

2. **Convert $$2 \frac{1}{3}$$**:
   $$
   2 \frac{1}{3} = 2 \times 3 + 1 = 6 + 1 = \frac{7}{3}
   $$

3. **Convert $$1 \frac{5}{12}$$**:
   $$
   1 \frac{5}{12} = 1 \times 12 + 5 = 12 + 5 = \frac{17}{12}
   $$

### Step 2: Substitute Back into the Expression

Now we can rewrite the expression:
$$
3 \frac{3}{4} + 2 \frac{1}{3} - 1 \frac{5}{12} = \frac{15}{4} + \frac{7}{3} - \frac{17}{12}
$$

### Step 3: Find a Common Denominator

The least common multiple of the denominators $$4$$, $$3$$, and $$12$$ is $$12$$.

- Convert $$\frac{15}{4}$$ to twelfths:
  $$
  \frac{15}{4} = \frac{15 \times 3}{4 \times 3} = \frac{45}{12}
  $$

- Convert $$\frac{7}{3}$$ to twelfths:
  $$
  \frac{7}{3} = \frac{7 \times 4}{3 \times 4} = \frac{28}{12}
  $$

- $$\frac{17}{12}$$ is already in twelfths.

### Step 4: Combine the Fractions

Now we can combine:
$$
\frac{45}{12} + \frac{28}{12} - \frac{17}{12} = \frac{45 + 28 - 17}{12} = \frac{56}{12}
$$

### Step 5: Simplify the Result

Now simplify $$\frac{56}{12}$$:
$$
\frac{56 \div 4}{12 \div 4} = \frac{14}{3}
$$

### Step 6: Calculate the Denominator

Now we need to calculate the denominator:
$$
\frac{15}{4} + \frac{7}{3} + \frac{17}{12}
$$

Using the same common denominator of $$12$$:
- $$\frac{15}{4} = \frac{45}{12}$$
- $$\frac{7}{3} = \frac{28}{12}$$
- $$\frac{17}{12}$$ is already in twelfths.

Combine:
$$
\frac{45}{12} + \frac{28}{12} + \frac{17}{12} = \frac{45 + 28 + 17}{12} = \frac{90}{12}
$$

### Step 7: Simplify the Denominator

Now simplify $$\frac{90}{12}$$:
$$
\frac{90 \div 6}{12 \div 6} = \frac{15}{2}
$$

### Step 8: Final Calculation

Now we can substitute back into the original expression:
$$
\frac{\frac{56}{12}}{\frac{15}{2}} = \frac{56}{12} \times \frac{2}{15} = \frac{56 \times 2}{12 \times 15} = \frac{112}{180}
$$

### Step 9: Simplify the Final Result

Now simplify $$\frac{112}{180}$$:
$$
\frac{112 \div 4}{180 \div 4} = \frac{28}{45}
$$

### Conclusion

The final result of the expression $$ \frac{3 \frac{3}{4}+2 \frac{1}{3}-1 \frac{5}{12}}{\frac{15}{4}+\frac{7}{3}+\frac{17}{12}} $$ is:
$$
\frac{28}{45}
$$

This does not equal $$ \frac{12}{12} + 1 = 2 $$. Therefore, the statement is incorrect.
The final result is $$ \frac{28}{45} $$, which is not equal to $$ \frac{12}{12} + 1 = 2 $$.

6. \( 3 \frac{3}{4}+2 \frac{1}{3}-1 \frac{5}{12} \) \( \frac{3 \frac{3}{4}+2 \frac{1}{2}-1 \frac{5}{12}}{\frac{15}{4}+\frac{7}{3}+\frac{17}{12}} \) \( =\frac{12}{12}+1 \)

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