Multiple ChoiceRationalize the denominator and simplify the radical expression.75−6\frac{\sqrt7}{5-\sqrt6}5−67 563views6rank
Multiple ChoiceRationalize the denominator and simplify the radical expression. 2−32+3\frac{2-\sqrt3}{2+\sqrt3}2+32−3421views3rank
Textbook QuestionCONCEPT PREVIEW Perform the operations mentally, and write the answers without doing intermediate steps. √25 + √64143views
Textbook QuestionCONCEPT PREVIEW Perform the operations mentally, and write the answers without doing intermediate steps. √6 • √6147views
Textbook QuestionCONCEPT PREVIEW Perform the operations mentally, and write the answers without doing intermediate steps. (√28 - √14) (√28 + √14)142views
Textbook QuestionUse the product and quotient rules for radicals to rewrite each expression. See Example 4. √3 • √5127views
Textbook QuestionUse the product and quotient rules for radicals to rewrite each expression. See Example 4. √3 • √27145views
Textbook QuestionUse the product and quotient rules for radicals to rewrite each expression. See Example 4. √7⁄16148views
Textbook QuestionUse the product and quotient rules for radicals to rewrite each expression. See Example 4. √4⁄50133views
Textbook QuestionUse the product and quotient rules for radicals to rewrite each expression. See Example 4. √5 √20115views
Textbook QuestionUse the product and quotient rules for radicals to rewrite each expression. See Example 4. 30√10 5√2116views
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 8148views
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 30133views
Textbook QuestionCONCEPT PREVIEW Perform the indicated operation, and write each answer in lowest terms 2x 10x —— • ——— 5 x²117views
Textbook QuestionCONCEPT PREVIEW Perform the indicated operation, and write each answer in lowest terms 3 7 —— + —— x x143views
Textbook QuestionCONCEPT PREVIEW Perform the indicated operation, and write each answer in lowest terms 2x x —— + —— 5 4120views
Textbook QuestionFind the domain of each rational expression. See Example 1. 3x + 7 ——————— (4x + 2) (x - 1)132views
Textbook QuestionFind the domain of each rational expression. See Example 1. 12 —————— x² + 5x + 6142views
Textbook QuestionFind the domain of each rational expression. See Example 1. x² - 1 ———— x + 1133views
Textbook QuestionFind the domain of each rational expression. See Example 1. x³ - 1 ———— x - 1143views
Textbook QuestionWrite each rational expression in lowest terms. See Example 2. 8x² + 16x 4x²133views
Textbook QuestionWrite each rational expression in lowest terms. See Example 2. 3 (3 - t) —————— (t + 5) (t - 3)137views
Textbook QuestionWrite each rational expression in lowest terms. See Example 2. 8k + 16 9k + 18128views
Textbook QuestionWrite each rational expression in lowest terms. See Example 2. m² - 4m + 4 m² + m - 6140views
Textbook QuestionWrite each rational expression in lowest terms. See Example 2. 8m² + 6m - 9 16m² - 9136views
Textbook QuestionMultiply or divide, as indicated. See Example 3. 2k + 8 3k + 12 ———— ÷ ———— 6 2151views
Textbook QuestionMultiply or divide, as indicated. See Example 3. x² + x 25 ———— • ———— 5 xy + y128views
Textbook QuestionMultiply or divide, as indicated. See Example 3. 4a + 12 a² - 9 ————— ÷ ————— 2a - 10 a² - a - 20150views
Textbook QuestionMultiply or divide, as indicated. See Example 3. m² + 3m + 2 m² + 5m + 6 ——————— ÷ ———————— m² + 5m + 4 m² + 10m + 24148views
Textbook QuestionMultiply or divide, as indicated. See Example 3. xz - xw + 2yz - 2yw 4z + 4w +xz +wx —————————— • ————————— z² - w² 16 - x²134views
Textbook QuestionAdd or subtract, as indicated. See Example 4. 17y + 3 -10y - 18 ———— - ————— 9y + 7 9y + 7122views
Textbook QuestionAdd or subtract, as indicated. See Example 4. x + y 2x ——— - ——— 2x - y y - 2x140views
Textbook QuestionAdd or subtract, as indicated. See Example 4. 4 1 12 ———— + —————— - ———— x + 1 x² - x + 1 x³ + 1146views
Textbook QuestionAdd or subtract, as indicated. See Example 4. 3x x —————— - ———— x² + x - 12 x² - 16147views
Textbook QuestionSimplify each complex fraction. See Examples 5 and 6. 5⁄8 + 2⁄3 ———— 7⁄3 - 1⁄4123views
Textbook QuestionSimplify each complex fraction. See Examples 5 and 6. ( -4⁄3 ) + 12⁄5 ———————— 1 - ( -4⁄3 ) (12⁄5)127views
Textbook QuestionSimplify each complex fraction. See Examples 5 and 6. x y — + — y x —————— x y — - — y x140views
Textbook QuestionSimplify each complex fraction. See Examples 5 and 6. 1 1 ——— - —— x + 1 x ———————— 1 —— x138views
Textbook QuestionSimplify each complex fraction. See Examples 5 and 6. y + 3 4 ———— - ———— y y - 1 —————————— y 1 ——— + —— y - 1 y130views
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?130views