Question

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

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Hermann

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**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)

1. Identify like terms:

2. Combine the coefficients:

3. Write the result with the same variable:

4. Identify like terms:

5. Combine the coefficients:

6. Write the result with the same variable:

**Canceling Fractions:**

1. Identify the GCF of 6 and 8, which is 2.

2. Divide both the numerator and the denominator by the GCF:

3. Factor the numerator and find common factors in the expression:

4. Cancel the common factor:

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