Multiple ChoiceRationalize the denominator and simplify the radical expression.75−6\frac{\sqrt7}{5-\sqrt6}5−67 580views6rank
Multiple ChoiceRationalize the denominator and simplify the radical expression. 2−32+3\frac{2-\sqrt3}{2+\sqrt3}2+32−3431views2rank
Textbook QuestionCONCEPT PREVIEW Perform the operations mentally, and write the answers without doing intermediate steps. √25 + √64154views
Textbook QuestionCONCEPT PREVIEW Perform the operations mentally, and write the answers without doing intermediate steps. √6 • √6160views
Textbook QuestionCONCEPT PREVIEW Perform the operations mentally, and write the answers without doing intermediate steps. (√28 - √14) (√28 + √14)154views
Textbook QuestionUse the product and quotient rules for radicals to rewrite each expression. See Example 4. √3 • √5136views
Textbook QuestionUse the product and quotient rules for radicals to rewrite each expression. See Example 4. √3 • √27157views
Textbook QuestionUse the product and quotient rules for radicals to rewrite each expression. See Example 4. √7⁄16158views
Textbook QuestionUse the product and quotient rules for radicals to rewrite each expression. See Example 4. √4⁄50144views
Textbook QuestionUse the product and quotient rules for radicals to rewrite each expression. See Example 4. √5 √20129views
Textbook QuestionUse the product and quotient rules for radicals to rewrite each expression. See Example 4. 30√10 5√2128views
Textbook QuestionFor 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 = 6 - √2 • 6 + √2 = 36 - 2 = 34 = 17 . 4 4 6 + √2 4(6 + √2) 4(6 + √2) 2(6 + √2) Rationalize each numerator. 6 - √3 8158views
Textbook QuestionFor 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 = 6 - √2 • 6 + √2 = 36 - 2 = 34 = 17 . 4 4 6 + √2 4(6 + √2) 4(6 + √2) 2(6 + √2) Rationalize each numerator. 2√10 + √7 30142views
Textbook QuestionCONCEPT PREVIEW Perform the indicated operation, and write each answer in lowest terms 2x 10x —— • ——— 5 x²128views
Textbook QuestionCONCEPT PREVIEW Perform the indicated operation, and write each answer in lowest terms 3 7 —— + —— x x160views
Textbook QuestionCONCEPT PREVIEW Perform the indicated operation, and write each answer in lowest terms 2x x —— + —— 5 4131views
Textbook QuestionFind the domain of each rational expression. See Example 1. 3x + 7 ——————— (4x + 2) (x - 1)141views
Textbook QuestionFind the domain of each rational expression. See Example 1. 12 —————— x² + 5x + 6156views
Textbook QuestionFind the domain of each rational expression. See Example 1. x² - 1 ———— x + 1143views
Textbook QuestionFind the domain of each rational expression. See Example 1. x³ - 1 ———— x - 1157views
Textbook QuestionWrite each rational expression in lowest terms. See Example 2. 8x² + 16x 4x²145views
Textbook QuestionWrite each rational expression in lowest terms. See Example 2. 3 (3 - t) —————— (t + 5) (t - 3)151views
Textbook QuestionWrite each rational expression in lowest terms. See Example 2. 8k + 16 9k + 18139views
Textbook QuestionWrite each rational expression in lowest terms. See Example 2. m² - 4m + 4 m² + m - 6155views
Textbook QuestionWrite each rational expression in lowest terms. See Example 2. 8m² + 6m - 9 16m² - 9150views
Textbook QuestionMultiply or divide, as indicated. See Example 3. 2k + 8 3k + 12 ———— ÷ ———— 6 2163views
Textbook QuestionMultiply or divide, as indicated. See Example 3. x² + x 25 ———— • ———— 5 xy + y142views
Textbook QuestionMultiply or divide, as indicated. See Example 3. 4a + 12 a² - 9 ————— ÷ ————— 2a - 10 a² - a - 20163views
Textbook QuestionMultiply or divide, as indicated. See Example 3. m² + 3m + 2 m² + 5m + 6 ——————— ÷ ———————— m² + 5m + 4 m² + 10m + 24169views
Textbook QuestionMultiply or divide, as indicated. See Example 3. xz - xw + 2yz - 2yw 4z + 4w +xz +wx —————————— • ————————— z² - w² 16 - x²166views
Textbook QuestionAdd or subtract, as indicated. See Example 4. 17y + 3 -10y - 18 ———— - ————— 9y + 7 9y + 7134views
Textbook QuestionAdd or subtract, as indicated. See Example 4. x + y 2x ——— - ——— 2x - y y - 2x155views
Textbook QuestionAdd or subtract, as indicated. See Example 4. 4 1 12 ———— + —————— - ———— x + 1 x² - x + 1 x³ + 1159views
Textbook QuestionAdd or subtract, as indicated. See Example 4. 3x x —————— - ———— x² + x - 12 x² - 16160views
Textbook QuestionSimplify each complex fraction. See Examples 5 and 6. 5⁄8 + 2⁄3 ———— 7⁄3 - 1⁄4133views
Textbook QuestionSimplify each complex fraction. See Examples 5 and 6. ( -4⁄3 ) + 12⁄5 ———————— 1 - ( -4⁄3 ) (12⁄5)133views
Textbook QuestionSimplify each complex fraction. See Examples 5 and 6. x y — + — y x —————— x y — - — y x151views
Textbook QuestionSimplify each complex fraction. See Examples 5 and 6. 1 1 ——— - —— x + 1 x ———————— 1 —— x153views
Textbook QuestionSimplify each complex fraction. See Examples 5 and 6. y + 3 4 ———— - ———— y y - 1 —————————— y 1 ——— + —— y - 1 y140views
Textbook Question(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. 7 - x Distance = ——————— 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 7 - 0.6 Distance = ————————— ≈ 3, which represents 3000 mi. 0.639(0.6) + 1.75 (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?144views