1. Warm-Up Exercises ANSWER 180 2. Find the least common multiple of 20 and 45. 1. Add 7 20 9 + ANSWER 4 5

2. Warm-Up Exercises EXAMPLE 1 Add or subtract with like denominators Perform the indicated operation. 7 4x4x + 3 4x4x a. 2x2x x + 6 – 5 b. SOLUTION 7 4x4x + 3 4x4x a. = 7 + 3 4x4x 10 4x4x = 5 2x2x = Add numerators and simplify result. x + 6 2x – 5 = 2x2x x + 6 5 – b. Subtract numerators.

3. Warm-Up Exercises GUIDED PRACTICE Perform the indicated operation and simplify. 1. 7 12x − 5 2. 2 3x 2 + 1 3x23x2 3. 4x x–2 – x 4. 2x 2 x 2 +1 + 2 1 6x6x ANSWER 1 x 2 ANSWER 3x x – 2 ANSWER 2

4. Warm-Up Exercises EXAMPLE 2 Find a least common multiple (LCM) Find the least common multiple of 4x 2 –16 and 6x 2 –24x + 24. SOLUTION STEP 1 Factor each polynomial. Write numerical factors as products of primes. 4x 2 – 16 = 4(x 2 – 4) = (2 2 )(x + 2)(x – 2) 6x 2 – 24x + 24 = 6(x 2 – 4x + 4) = (2)(3)(x – 2) 2

5. Warm-Up Exercises EXAMPLE 2 Find a least common multiple (LCM) STEP 2 Form the LCM by writing each factor to the highest power it occurs in either polynomial. LCM = (2 2 )(3)(x + 2)(x – 2) 2 = 12(x + 2)(x – 2) 2

6. Warm-Up Exercises GUIDED PRACTICE Find the least common multiple of the polynomials. 5. 5x 3 and 10x 2 –15x LCM = 5x 3 (2x – 3) ANSWER 6. 8x – 16 and 12x 2 + 12x – 72 LCM = 24(x – 2)(x + 3) ANSWER

7. Warm-Up Exercises EXAMPLE 3 Add with unlike denominators Add: 9x29x2 7 + x 3x 2 + 3x SOLUTION To find the LCD, factor each denominator and write each factor to the highest power it occurs. Note that 9x 2 = 3 2 x 2 and 3x 2 + 3x = 3x(x + 1), so the LCD is 3 2 x 2 (x + 1) = 9x 2 (x + 1). Factor second denominator. 7 9x29x2 x 3x 2 + 3x = 7 9x29x2 + 3x(x + 1) x + LCD is 9x 2 (x + 1). 7 9x29x2 x + 1 + 3x(x + 1) x 3x3x 3x3x =

8. Warm-Up Exercises EXAMPLE 3 Add with unlike denominators Multiply. Add numerators. 3x 2 + 7x + 7 9x 2 (x + 1) = 7x + 7 9x 2 (x + 1) 3x23x2 +=