1. Adding and Subtracting Rational Expressions
LESSON 8–2
Adding and Subtracting Rational Expressions

2. A. B. C. D.
5-Minute Check 3

3. Mathematical Processes A2.1(A), A2.1(B)
Targeted TEKS
A2.7(F) Determine the sum, difference, product, and quotient of rational expressions with integral exponents of degree one
and of degree two.
Mathematical Processes
A2.1(A), A2.1(B)
TEKS

4. You added and subtracted polynomial expressions.
Determine the LCM of polynomials.
Add and subtract rational expressions.
Then/Now

5. B. Find the LCM of x3 – x2 – 2x and x2 – 4x + 4.
LCM of Monomials and Polynomials
B. Find the LCM of x3 – x2 – 2x and x2 – 4x + 4.
x3 – x2 – 2x = x(x + 1)(x – 2) Factor the first polynomial.
x2 – 4x + 4 = (x – 2)2 Factor the second polynomial.
LCM = x(x + 1)(x – 2)2 Use each factor the greatest number of times it appears as a factor.
Answer: x(x + 1)(x – 2)2
Example 1B

6. B. Find the LCM of x3 + 2x2 – 3x and x2 + 6x + 9.
A. x(x + 3)2(x – 1)
B. x(x + 3)(x – 1)
C. x(x – 1)
D. (x + 3)(x – 1)
Example 1B

7. Concept

8. Simplify each numerator and denominator.
Monomial Denominators
Simplify
The LCD is 42a2b2.
Simplify each numerator and denominator.
Add the numerators.
Example 2

9. Monomial Denominators
Answer:
Example 2

10. Simplify A. B. C. D.
Example 2

11. Factor the denominators.
Polynomial Denominators
Simplify
Factor the denominators.
The LCD
is 6(x – 5).
Subtract the numerators.
Example 3

12. Distributive Property
Polynomial Denominators
Distributive Property
Combine like terms.
Simplify.
Simplify.
Answer:
Example 3

13. Simplify A. B. C. D.
Example 3

14. The LCD of the numerator is ab. The LCD of the denominator is b.
Complex Fractions with Different LCDs
Simplify
The LCD of the numerator is ab. The LCD of the denominator is b.
Example 4

15. Simplify the numerator and denominator.
Complex Fractions with Different LCDs
Simplify the numerator and denominator.
Write as a division expression.
Multiply by the reciprocal of the divisor.
Simplify.
Example 4

16. Complex Fractions with Different LCDs
Answer:
Example 4

17. Simplify
A. B. –1
C. D.
Example 4

18. The LCD of all of the denominators is xy. Multiply by
Complex Fractions with Same LCD
Simplify
The LCD of all of the denominators is xy. Multiply by
Distribute xy.
Example 5

19. Complex Fractions with Same LCD
Answer:
Example 5

20. Simplify
A. B.
C. D.
Example 5

21. Adding and Subtracting Rational Expressions
LESSON 8–2
Adding and Subtracting Rational Expressions