What are all the rules to combing like terms and canceling fractions

**Combining Like Terms:**
1. Identify like terms:
3x and 4x are like terms because they have the same variable, x.
2. Combine the coefficients:
3 + 4 = 7
3. Write the result with the same variable:
3x + 4x = 7x

4. Identify like terms:
5y^2 and -2y^2 are like terms because they have the same variable and power, y^2.
5. Combine the coefficients:
5 - 2 = 3
6. Write the result with the same variable:
5y^2 - 2y^2 = 3y^2

**Canceling Fractions:**
1. Identify the GCF of 6 and 8, which is 2.
2. Divide both the numerator and the denominator by the GCF:
\frac{6}{8} = \frac{6 \div 2}{8 \div 2} = \frac{3}{4}

3. Factor the numerator and find common factors in the expression:
\frac{x^2 - 9}{x + 3} = \frac{(x + 3)(x - 3)}{x + 3}
4. Cancel the common factor:
\frac{(x + 3)(x - 3)}{x + 3} = x - 3 \quad (\text{provided that } x \neq -3)