0. Review of College Algebra

Multiply or divide, as indicated. See Example 3. ((4a + 12) / (2a - 10)) ÷ ((a² - 9) / (a² - a - 20))

Add or subtract, as indicated. See Example 4. (3/2k) + (5/3k)

CONCEPT PREVIEW Perform the operations mentally, and write the answers without doing intermediate steps. (√28 - √14) (√28 + √14)

Find the domain of each rational expression. See Example 1. (x + 3) / (x - 6)

For Individual or Group Work (Exercises 147 – 150)In calculus, it is sometimes desirable to rationalize a numerator. To do this, we multiply the numerator and the denominator by the conjugate of the numerator. For example, (6 - √2)/4 = (6 - √2)/4 × (6 + √2)/(6 + √2) = (36 - 2)/(4(6 + √2)) = 34/(4(6 + √2)) = 17/(2(6 + √2)) = 17/(6 + √2). Rationalize each numerator. (6 - √3)/8

Multiply or divide, as indicated. See Example 3. ((m² + 3m + 2) / (m² + 5m + 4)) ÷ ((m² + 5m + 6) / (m² + 10m + 24))

Add or subtract, as indicated. See Example 4. ((17y + 3)/(9y + 7)) - ((-10y - 18)/(9y + 7 ))

Add or subtract, as indicated. See Example 4. (3/a - 2) - (1/2 - a)

Rationalize each denominator. See Example 8. 18 —— √27

Simplify each complex fraction. See Examples 5 and 6. (1/(x + 1) − 1/x) / (1/x)

Find the domain of each rational expression. See Example 1. 12 / (x² + 5x + 6)

Find each square root. See Example 1. √4⁄25

Use the product and quotient rules for radicals to rewrite each expression. See Example 4. √3 • √5

Find each root. See Example 3. -∛512