Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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1.
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The non-permissible value(s) for the rational expressions  is
(are) A | x ¹  , x ¹ - | C | x ¹
 | B | x ¹  | D | x ¹ 4 |
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2.
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The non-permissible value(s) for the expression  is (are) A | x ¹  | C | x ¹  and x ¹
–7 | B |  | D | there are no restrictions |
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3.
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What is  in simplest form? State any non-permissible values.
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4.
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What is the simplified version of the rational expression  ?
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5.
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When fully simplified, ignoring non-permissible values,  is equal to
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6.
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When fully simplified,  is equal to
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7.
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When fully simplified, ignoring restrictions on the variable,  is equal to
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8.
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Simplify the rational expression  .
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9.
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Simplify  . State any non-permissible values.
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10.
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In a biathlon race, Murray must cycle 60 km and then run 20 km. Using  as
his cycling speed and  as his running speed, what is the correct simplified
expression for the total time needed to complete the race?
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Short Answer
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Determine if the function f(x) is the simplified form of g(x). If it is,
state the non-permissible values. If it is not, determine the
corrected simplified form, including the non-permissible values.
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1.
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2.
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Simplify each expression and state any non-permissible values.
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3.
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Problem
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1.
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a) Simplify the expressions in each pair. i)  ii)
 b) Are the functions in each pair in part a) equivalent? Explain your
answer.
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2.
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Alice is in a 20-km race. She always runs the first half at an average speed of
2 km/h faster than the second half.
a) Let x represent her speed in the first half.
Determine a simplified expression in terms of x for the total time needed to run the
race.
b) If Alice runs the first half at 10 km/h, how long will it take her to run the
race, to the nearest tenth of an hour?
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