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Problem 49
Add or subtract, as indicated. See Example 4. (3/2k) + (5/3k)
Problem 51
Add or subtract, as indicated. See Example 4. (1/6m) + (2/5m) + (4/m)
Problem 53
Add or subtract, as indicated. See Example 4. (1/a)+(b/a²)
Problem 55
Add or subtract, as indicated. See Example 4. (5/12x²y) - (11/6xy)
Problem 57
Add or subtract, as indicated. See Example 4. ((17y + 3)/(9y + 7)) - ((-10y - 18)/(9y + 7 ))
Problem 59
Add or subtract, as indicated. See Example 4. (1/(x + z)) + (1/(x - z))
Problem 61
Add or subtract, as indicated. See Example 4. (3/a - 2) - (1/2 - a)
Problem 65
Add or subtract, as indicated. See Example 4. 4/(x+1) + 1/(x² - x + 1) - 12/(x³ + 1)
Problem 67
Add or subtract, as indicated. See Example 4. (3x)/(x² + x − 12) − x/(x² − 16) + x
Problem 69
Simplify each complex fraction. See Examples 5 and 6. (−4/3) ÷ (2/9)
Problem 71
Simplify each complex fraction. See Examples 5 and 6. (y/r) ÷ (x/y)
Problem 73
Simplify each complex fraction. See Examples 5 and 6. (5/8 + 2/3) ÷ (7/1 − 1/4)
Problem 75
Simplify each complex fraction. See Examples 5 and 6. [ (−4/3) + 12/5 ] / [ 1 − (−4/3)(12/5) ]
Problem 79
Simplify each complex fraction. See Examples 5 and 6. (1 + 1/x) / (1 − 1/x)
Problem 83
Simplify each complex fraction. See Examples 5 and 6. (x/y + y/x) / (x/y − y/x)
Problem 87
Simplify each complex fraction. See Examples 5 and 6. (1/(x + 1) − 1/x) / (1/x)
Problem 91
Simplify each complex fraction. See Examples 5 and 6. [(y + 3)/y − 4/(y − 1)] / [(y/y + 1/y) / (y − 1) + 1/y]
Problem 93
(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?
Problem 7
CONCEPT PREVIEW Perform the operations mentally, and write the answers without doing intermediate steps. √25 + √64
Problem 9
CONCEPT PREVIEW Perform the operations mentally, and write the answers without doing intermediate steps. √6 • √6
Problem 10
CONCEPT PREVIEW Perform the operations mentally, and write the answers without doing intermediate steps. (√28 - √14) (√28 + √14)
Problem 13
Find each square root. See Example 1. √100
Problem 17
Find each square root. See Example 1. -√256
Problem 19
Find each square root. See Example 1. √4⁄25
Problem 21
Find each square root. See Example 1. -√144⁄121
Problem 25
Find each square root. See Example 1. √-121
Problem 29
Find the square of each radical expression. See Example 2. -√19
Problem 31
Find the square of each radical expression. See Example 2. √2 /3
Problem 33
Find the square of each radical expression. See Example 2. √3x² + 4
Problem 37
Find each root. See Example 3. -∛512