0. Review of College Algebra

Simplify each complex fraction. See Examples 5 and 6. [(y + 3)/y − 4/(y − 1)] / [(y/y + 1/y) / (y − 1) + 1/y]

Simplify each radical. See Example 5. 3√27

Multiply. See Example 7. (√2 + 1) (√3 + 1)

Write each rational expression in lowest terms. See Example 2. (8m² + 6m - 9) / (16m² - 9)

Use the product and quotient rules for radicals to rewrite each expression. See Example 4. √7⁄16

Use the product and quotient rules for radicals to rewrite each expression. See Example 4. 30√10 / 5√2

(Modeling) Distance from the Origin of the Nile River The Nile River in Africa is about 4000 mi long. The Nile begins as an outlet of Lake Victoria at an altitude of 7000 ft above sea level and empties into the Mediterranean Sea at sea level (0 ft). The distance from its origin in thousands of miles is related to its height above sea level in thousands of feet (x) by the following formula.

Distance = (7 − x) / (0.639x + 1.75)

For example, when the river is at an altitude of 600 ft, x = 0.6 (thousand), and the distance from the origin is

Distance ≈ (7 − 0.6) / (0.639 × 0.6 + 1.75) ≈ 3, which represents 3000 mi. (Data from The World Almanac and Book of Facts.) What is the distance from the origin of the Nile when the river has an altitude of 7000 ft?

Find the square of each radical expression. See Example 2. √3x² + 4

Multiply. See Example 7. √6 (3 + √2)

Add or subtract, as indicated. See Example 6. √6 + √7

Use the product and quotient rules for radicals to rewrite each expression. See Example 4. √4⁄50

Add or subtract, as indicated. See Example 4. (3x)/(x² + x − 12) − x/(x² − 16) + x

Find each square root. See Example 1. √-121

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