Multiple ChoiceRationalize the denominator and simplify the radical expression.75−6\frac{\sqrt7}{5-\sqrt6}5−67 579views6rank
Multiple ChoiceRationalize the denominator and simplify the radical expression. 2−32+3\frac{2-\sqrt3}{2+\sqrt3}2+32−3430views2rank
Textbook QuestionCONCEPT PREVIEW Perform the operations mentally, and write the answers without doing intermediate steps. √25 + √64153views
Textbook QuestionCONCEPT PREVIEW Perform the operations mentally, and write the answers without doing intermediate steps. √6 • √6159views
Textbook QuestionCONCEPT PREVIEW Perform the operations mentally, and write the answers without doing intermediate steps. (√28 - √14) (√28 + √14)153views
Textbook QuestionUse the product and quotient rules for radicals to rewrite each expression. See Example 4. √3 • √5135views
Textbook QuestionUse the product and quotient rules for radicals to rewrite each expression. See Example 4. √3 • √27156views
Textbook QuestionUse the product and quotient rules for radicals to rewrite each expression. See Example 4. √7⁄16157views
Textbook QuestionUse the product and quotient rules for radicals to rewrite each expression. See Example 4. √4⁄50143views
Textbook QuestionUse the product and quotient rules for radicals to rewrite each expression. See Example 4. √5 √20128views
Textbook QuestionUse the product and quotient rules for radicals to rewrite each expression. See Example 4. 30√10 5√2127views
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 8157views
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 30141views
Textbook QuestionCONCEPT PREVIEW Perform the indicated operation, and write each answer in lowest terms 2x 10x —— • ——— 5 x²126views
Textbook QuestionCONCEPT PREVIEW Perform the indicated operation, and write each answer in lowest terms 3 7 —— + —— x x158views
Textbook QuestionCONCEPT PREVIEW Perform the indicated operation, and write each answer in lowest terms 2x x —— + —— 5 4130views
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 + 6155views
Textbook QuestionFind the domain of each rational expression. See Example 1. x² - 1 ———— x + 1141views
Textbook QuestionFind the domain of each rational expression. See Example 1. x³ - 1 ———— x - 1156views
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)150views
Textbook QuestionWrite each rational expression in lowest terms. See Example 2. 8k + 16 9k + 18138views
Textbook QuestionWrite each rational expression in lowest terms. See Example 2. m² - 4m + 4 m² + m - 6154views
Textbook QuestionWrite each rational expression in lowest terms. See Example 2. 8m² + 6m - 9 16m² - 9149views
Textbook QuestionMultiply or divide, as indicated. See Example 3. 2k + 8 3k + 12 ———— ÷ ———— 6 2161views
Textbook QuestionMultiply or divide, as indicated. See Example 3. x² + x 25 ———— • ———— 5 xy + y141views
Textbook QuestionMultiply or divide, as indicated. See Example 3. 4a + 12 a² - 9 ————— ÷ ————— 2a - 10 a² - a - 20162views
Textbook QuestionMultiply or divide, as indicated. See Example 3. m² + 3m + 2 m² + 5m + 6 ——————— ÷ ———————— m² + 5m + 4 m² + 10m + 24167views
Textbook QuestionMultiply or divide, as indicated. See Example 3. xz - xw + 2yz - 2yw 4z + 4w +xz +wx —————————— • ————————— z² - w² 16 - x²165views
Textbook QuestionAdd or subtract, as indicated. See Example 4. 17y + 3 -10y - 18 ———— - ————— 9y + 7 9y + 7132views
Textbook QuestionAdd or subtract, as indicated. See Example 4. x + y 2x ——— - ——— 2x - y y - 2x154views
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 - 16159views
Textbook QuestionSimplify each complex fraction. See Examples 5 and 6. 5⁄8 + 2⁄3 ———— 7⁄3 - 1⁄4132views
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 x150views
Textbook QuestionSimplify each complex fraction. See Examples 5 and 6. 1 1 ——— - —— x + 1 x ———————— 1 —— x152views
Textbook QuestionSimplify each complex fraction. See Examples 5 and 6. y + 3 4 ———— - ———— y y - 1 —————————— y 1 ——— + —— y - 1 y139views
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