1. Operations on Rational Expressions
Digital Lesson
Operations on Rational Expressions

2. Rational expressions are fractions in which the numerator and denominator are polynomials and the denominator does not equal zero.
Example: Simplify
, x – 3  0
, x  3
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Rational Expressions

3. Multiplying Rational Expression
To multiply rational expressions:
1. Factor the numerator and denominator of each fraction.
2. Multiply the numerators and denominators of each fraction.
3. Divide by the common factors.
4. Write the answer in simplest form.
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Multiplying Rational Expression

4. Example: Multiplication
Multiply
Factor the numerator and denominator of each fraction.
Multiply.
Divide by the common factors.
Write the answer in simplest form.
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Example: Multiplication

5. Dividing Rational Expressions
To divide rational expressions:
1. Multiply the dividend by the reciprocal of the divisor. The reciprocal of is .
2. Multiply the numerators. Then multiply the denominators.
3. Divide by the common factors.
4. Write the answer in simplest form.
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Dividing Rational Expressions

6. Example: Divide . Multiply by the reciprocal of the divisor.
Factor and multiply.
Divide by the common factors.
Simplest form
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Example: Division

7. The least common multiple (LCM) of two or more numbers is the
least number that contains the prime factorization of each number.
Examples: 1. Find the LCM of 10 and 4.
10 = (5 • 2)
factors of 10
4 = (2 • 2)
LCM = 2 • 2 • 5
= 20
factors of 4
2. Find the LCM of 4x2 + 4x and x2 + 2x + 1.
4x2 + 4x = (4x)(x +1) = 2 • 2 x (x + 1)
x2 + 2x + 1 = (x +1)(x +1)
factors of x2 + 2x + 1
LCM = 2 • 2 x (x +1)(x +1)
= 4x3 + 8x2 + 4x
factors of 4x2 + 4x
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Least Common Multiple

8. Least Common Multiple of Denominators
Fractions can be expressed in terms of the least common multiple of their denominators.
Example: Write the fractions and in terms of the LCM of the denominators.
The LCM of the denominators is 12x2(x – 2).
LCM
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Least Common Multiple of Denominators

9. Adding and Subtracting Rational Expressions
To add rational expressions:
If necessary, rewrite the fractions with a common denominator.
2. Add the numerators of each fraction.
To subtract rational expressions:
If necessary, rewrite the fractions with a common denominator.
2. Subtract the numerators of each fraction.
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Adding and Subtracting Rational Expressions

10. Examples: Addition & Subtraction
Example: Add
Example: Subtract
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Examples: Addition & Subtraction

11. Different Denominators
Two rational expressions with different denominators can be added or subtracted after they are rewritten with a common denominator.
Example: Add
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Different Denominators

12. Example: Subtract . Add numerators. Factor. Divide. Simplest form
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Example: Subtract