0. Review of College Algebra

Rationalize each denominator. See Example 8. (√3 + 1)/(1 - √3)

Rationalize each denominator. See Example 8. (√2 - √3)/(√6 - √5)

Simplify. See Example 9. (-√2/3)/(√7/3)

Simplify. See Example 9. (√7/5)/(√3/10)

Simplify. See Example 9. (1/2)/(1 - (√5/2))

Simplify. See Example 9. (√3/2)/(1 - (√3/2))

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

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).

2√10 + √7 30

CONCEPT PREVIEW Perform the indicated operation, and write each answer in lowest terms (2x/5) • (10/x²)

CONCEPT PREVIEW Perform the indicated operation, and write each answer in lowest terms 2x/5 + x/4

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

Find the domain of each rational expression. See Example 1. (3x + 7) / (4x + 2) (x - 1)

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

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