Multiple ChoiceRationalize the denominator and simplify the radical expression.75−6\frac{\sqrt7}{5-\sqrt6}5−67 586views6rank
Multiple ChoiceRationalize the denominator and simplify the radical expression. 2−32+3\frac{2-\sqrt3}{2+\sqrt3}2+32−3436views2rank
Textbook QuestionCONCEPT PREVIEW Perform the operations mentally, and write the answers without doing intermediate steps. √25 + √64160views
Textbook QuestionCONCEPT PREVIEW Perform the operations mentally, and write the answers without doing intermediate steps. √6 • √6167views
Textbook QuestionCONCEPT PREVIEW Perform the operations mentally, and write the answers without doing intermediate steps. (√28 - √14) (√28 + √14)160views
Textbook QuestionUse the product and quotient rules for radicals to rewrite each expression. See Example 4. √3 • √5144views
Textbook QuestionUse the product and quotient rules for radicals to rewrite each expression. See Example 4. √3 • √27165views
Textbook QuestionUse the product and quotient rules for radicals to rewrite each expression. See Example 4. √7⁄16165views
Textbook QuestionUse the product and quotient rules for radicals to rewrite each expression. See Example 4. √4⁄50152views
Textbook QuestionUse the product and quotient rules for radicals to rewrite each expression. See Example 4. √5 √20136views
Textbook QuestionUse the product and quotient rules for radicals to rewrite each expression. See Example 4. 30√10 5√2137views
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 8163views
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 30149views
Textbook QuestionCONCEPT PREVIEW Perform the indicated operation, and write each answer in lowest terms 2x 10x —— • ——— 5 x²134views
Textbook QuestionCONCEPT PREVIEW Perform the indicated operation, and write each answer in lowest terms 3 7 —— + —— x x165views
Textbook QuestionCONCEPT PREVIEW Perform the indicated operation, and write each answer in lowest terms 2x x —— + —— 5 4138views
Textbook QuestionFind the domain of each rational expression. See Example 1. 3x + 7 ——————— (4x + 2) (x - 1)147views
Textbook QuestionFind the domain of each rational expression. See Example 1. 12 —————— x² + 5x + 6162views
Textbook QuestionFind the domain of each rational expression. See Example 1. x² - 1 ———— x + 1149views
Textbook QuestionFind the domain of each rational expression. See Example 1. x³ - 1 ———— x - 1162views
Textbook QuestionWrite each rational expression in lowest terms. See Example 2. 8x² + 16x 4x²149views
Textbook QuestionWrite each rational expression in lowest terms. See Example 2. 3 (3 - t) —————— (t + 5) (t - 3)158views
Textbook QuestionWrite each rational expression in lowest terms. See Example 2. 8k + 16 9k + 18146views
Textbook QuestionWrite each rational expression in lowest terms. See Example 2. m² - 4m + 4 m² + m - 6163views
Textbook QuestionWrite each rational expression in lowest terms. See Example 2. 8m² + 6m - 9 16m² - 9155views
Textbook QuestionMultiply or divide, as indicated. See Example 3. 2k + 8 3k + 12 ———— ÷ ———— 6 2169views
Textbook QuestionMultiply or divide, as indicated. See Example 3. x² + x 25 ———— • ———— 5 xy + y147views
Textbook QuestionMultiply or divide, as indicated. See Example 3. 4a + 12 a² - 9 ————— ÷ ————— 2a - 10 a² - a - 20169views
Textbook QuestionMultiply or divide, as indicated. See Example 3. m² + 3m + 2 m² + 5m + 6 ——————— ÷ ———————— m² + 5m + 4 m² + 10m + 24175views
Textbook QuestionMultiply or divide, as indicated. See Example 3. xz - xw + 2yz - 2yw 4z + 4w +xz +wx —————————— • ————————— z² - w² 16 - x²169views
Textbook QuestionAdd or subtract, as indicated. See Example 4. 17y + 3 -10y - 18 ———— - ————— 9y + 7 9y + 7139views
Textbook QuestionAdd or subtract, as indicated. See Example 4. x + y 2x ——— - ——— 2x - y y - 2x159views
Textbook QuestionAdd or subtract, as indicated. See Example 4. 4 1 12 ———— + —————— - ———— x + 1 x² - x + 1 x³ + 1164views
Textbook QuestionAdd or subtract, as indicated. See Example 4. 3x x —————— - ———— x² + x - 12 x² - 16166views
Textbook QuestionSimplify each complex fraction. See Examples 5 and 6. 5⁄8 + 2⁄3 ———— 7⁄3 - 1⁄4140views
Textbook QuestionSimplify each complex fraction. See Examples 5 and 6. ( -4⁄3 ) + 12⁄5 ———————— 1 - ( -4⁄3 ) (12⁄5)141views
Textbook QuestionSimplify each complex fraction. See Examples 5 and 6. x y — + — y x —————— x y — - — y x155views
Textbook QuestionSimplify each complex fraction. See Examples 5 and 6. 1 1 ——— - —— x + 1 x ———————— 1 —— x159views
Textbook QuestionSimplify each complex fraction. See Examples 5 and 6. y + 3 4 ———— - ———— y y - 1 —————————— y 1 ——— + —— y - 1 y146views
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?151views