Exam 6: Reducing Rational Expressions to Lowest Terms

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Reduce the following rational expression to lowest terms, if possible. Reduce the following rational expression to lowest terms, if possible.

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Simplify the expression. Work inside parentheses first, and then divide out common factors. Simplify the expression. Work inside parentheses first, and then divide out common factors.

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To reduce the following rational expression to lowest terms, you will have to use factoring by grouping. Be sure to factor each numerator and denominator completely before dividing out any common factors. (Remember, factoring by grouping takes two steps.) To reduce the following rational expression to lowest terms, you will have to use factoring by grouping. Be sure to factor each numerator and denominator completely before dividing out any common factors. (Remember, factoring by grouping takes two steps.)

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Perform the indicated operation. Reduce your answer to lowest terms. Perform the indicated operation. Reduce your answer to lowest terms.

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Perform the indicated operation. Reduce your answer to lowest terms. Perform the indicated operation. Reduce your answer to lowest terms.

(Multiple Choice)
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Perform the indicated operation. Perform the indicated operation.

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The sum of the reciprocals of two consecutive integers is The sum of the reciprocals of two consecutive integers is   . Find the two integers. . Find the two integers.

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Perform the indicated operation. Reduce your answer to lowest terms. Perform the indicated operation. Reduce your answer to lowest terms.

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Simplify the complex fraction. Simplify the complex fraction.

(Multiple Choice)
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Perform the indicated operation. Perform the indicated operation.

(Multiple Choice)
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To reduce the following rational expression to lowest terms, you will have to use factoring by grouping. Be sure to factor each numerator and denominator completely before dividing out any common factors. (Remember, factoring by grouping takes two steps.) To reduce the following rational expression to lowest terms, you will have to use factoring by grouping. Be sure to factor each numerator and denominator completely before dividing out any common factors. (Remember, factoring by grouping takes two steps.)

(Multiple Choice)
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Perform the indicated operation. Perform the indicated operation.

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Solve the following equation. Be sure to check each answer in the original equation if you multiply both sides by an expression that contains the variable. Solve the following equation. Be sure to check each answer in the original equation if you multiply both sides by an expression that contains the variable.   x = __________ x = __________

(Short Answer)
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Simplify the complex fraction. Simplify the complex fraction.

(Multiple Choice)
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Simplify the complex fraction. Simplify the complex fraction.

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Solve the following equation. Be sure to check each answer in the original equation if you multiply both sides by an expression that contains the variable. Solve the following equation. Be sure to check each answer in the original equation if you multiply both sides by an expression that contains the variable.   a = __________ a = __________

(Short Answer)
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A bathtub can be filled by the cold water faucet in 15 minutes and by the hot water faucet in 18 minutes. How long does it take to fill the tub if both faucets are open?

(Multiple Choice)
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Solve the following equation. Be sure to check each answer in the original equation if you multiply both sides by an expression that contains the variable. Solve the following equation. Be sure to check each answer in the original equation if you multiply both sides by an expression that contains the variable.   y = __________ y = __________

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Perform the indicated operation. Perform the indicated operation.

(Multiple Choice)
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If 100 grams of ice cream contains 13 grams of fat, how much fat is in 650 grams of ice cream? __________ grams

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