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

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

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

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

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

Concept

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

Monomial Denominators Answer: Example 2

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

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

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

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

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

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

Complex Fractions with Different LCDs Answer: Example 4

Simplify . A. B. –1 C. D. Example 4

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

Complex Fractions with Same LCD Answer: Example 5

Simplify A. B. C. D. Example 5

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