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x−3
x+3 PRE-CALCULUS 11 Unit 5 – Day 2: RATIONAL EXPRESSIONS (Part 2) RATIONAL EXPRESSIONS
Rational expressions can be used to model many situations. example: The volume of a right rectangular prism in cubic centimetres is given by the
polynomial x3 + 4x2 − 12x , where x is the width of the prism's base in
centimetres. The length of the prism's base is (x + 6) centimetres.
a)
b) Simplify the rational expression. What does this expression represent? c) solution Write a rational expression that will represent the prism's height.
State the permissible values for x . a) The volume of a right rectangular prism is the product of its base area
and its height.
The base area is the product of the base's width and length.
The prism's height must be the result of dividing its volume by the
product of the base's width and length.
The prism's height is b) To simplify the numerator must be factored. x3 + 4 x2 − 12 x
x( x + 6)
x( x2 + 4 x − 12)
x( x + 6)
x( x + 6)( x − 2)
x( x + 6) Divide the numerator and denominator by
the common factors. x−2 x − 2 represents the prism's height in centimetres. c) All the dimensions must be longer than 0 cm. x>2 Unit 5: Day 2 notes - Rational Expressions (Part 2) Page 2 of 2 exercise: The current of a river is c miles per hour. A boat's speed in still water is
12 miles per hour.
a) Write an expression that will represent the time required for this boat to
travel 150 miles downriver. b) Write an expression that will represent the time required for this boat to
travel 150 miles upriver. c) Write an expression that will represent the difference in the times
required for this boat to travel 150 miles downriver and upriver. [Answer: ( ) 150 hours, 150 hours, 150 − 150 hours
12 − c
12 − c 12 + c
12 + c We will be multiplying, dividing, adding, and subtracting rational expressions.
You must know how to do these operations with rational numbers (fractions). PRE-CALCULUS 11 Unit 5 – Day 3: MULTIPLYING AND DIVIDING RATIONAL EXPRESSIONS MULTIPLYIN...

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