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This appears to be a math homework assignment related to "Calculs numériques" and "Calcul littéral." Let's break down the tasks for each exercise.

### Exercise 1:
You are asked to work with two mathematical expressions:
- \( A = 1 - \frac{2}{3} + \frac{5}{6} - \frac{3}{4} \)
- \( B = \frac{4 \times 10^3 \times 0.3 \times 10^{-2}}{6 \times 10^2} \)

1. **Write \( A \) as an irreducible fraction.**
   You need to perform the addition and subtraction of fractions and simplify the result.

2. **Write \( B \) in scientific notation.**
   You are required to calculate \( B \) and express it in scientific notation.

### Exercise 2:
This is a calculation program. The program instructs you to:
- Choose a starting number, \( x \).
- Add 1 to the number.
- Square the result.
- Subtract the square of the starting number.
- Write down the final result.

1. **Part 1:**
   - \( (a) \) Verify that when the starting number is 1, the result is 3.
   - \( (b) \) Determine the result when the starting number is 2.
   
2. **Part 2:**
   - Express the final result as a function of \( x \) based on the given steps in the program.
   
3. **Part 3:**
   - Expand and simplify the expression \( P = (x + 1)^2 - x^2 \).

4. **Part 4:**
   - Find the starting number \( x \) that gives a final result of 15.

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Would you like a detailed step-by-step solution to each part of these exercises? Let me know if you have any specific questions or if you'd like to proceed with a particular one.

### Relative Questions:
1. How do you add and subtract fractions with different denominators?
2. What are the key steps for simplifying a fraction to its irreducible form?
3. How do you convert a number into scientific notation?
4. How can we generalize a sequence of operations into an algebraic expression?
5. What methods can you use to solve equations involving squared terms?

### Tip:
When working with scientific notation, always ensure the final result has one non-zero digit before the decimal point, and adjust the exponent accordingly.

Solve math exercises involving calculations with fractions and scientific notation, as well as a calculation program involving algebraic expressions.

Learn how to simplify complex fractions, express numbers in scientific notation, and expand algebraic expressions. This exercise is suitable for Grades 8-10 and covers key concepts in fractions, scientific notation, and algebra.

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