McGraw-Hill Ryerson
Pre-Calculus 11
Chapter 6
Rational Expressions and Equations
Section 6.1
Click here to begin the lesson
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Recapping:
Your turn p. 312,
315, simplifying
316; simplifying and finding exceptions with
two variables.
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p. 312
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p. 315
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p. 316
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Chapter
6
Non-Permissible Values
For each rational expression, determine all non-permissible values. State the domain for
each expression. Use the pen tool to write your answers. Click on the expression to reveal
the answer.
p2  25
2. 2
p  10 p  25
3
3. 3
x
The non-permissible value is
x  2
The domain is
The non-permissible value is
p5
The domain is
The non-permissible value is
x 0
The domain is
x | x  2, x  R
p | p  5, p  R
x | x  0, x  R
2x  y
4.
xy
2x 2  5y
5.
xy
The non-permissible values are
x  0 and y  0
The domain is
The non-permissible values are
xy
The domain is
x, y | x  0, y  0, x, y  R
x, y | x  y , x, y  R
Hint
7x
1.
8 x  16
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A non-permissible value is any value for a
variable that makes an expression undefined.
In a rational expression, it is a value that
results in a denominator of zero.
2x 2
6. 2
x 4
The non-permissible values are
x  2
The domain is
x | x  2, x  R
Chapter
6
Simplifying Rational Expressions
Identify each of the following as true or false.
1.
x4
 x  2, x  0
2
x 4  2x
2.
 x 3  2, x  0
x
x2  4
3.
 x  2, x  2
x 2
x 2  6x  8
4.
 x  4, x  2,4
x2
r2 4 r 2
5.

,r  R
5r  10
5
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3t 2  8t  4 t  2
2
6.

,
t

0,
6t 2  4t
2t
3
Chapter
Apply Rational Expressions
6
The area of a2 rectangular garden can be represented by the
polynomial x + 3x + 2 and its width by x + 1.
a) Write a rational expression that represents the length.
b) Write the expression in simplest form.
c) If x represents 1 unit of length, what is the ratio
length : width for this garden?
Click here for the solution.
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p. 317 #2 b, d
# 3 d, e, f
#4 b, c, f,
p. 318 #7, 8, c, d, f,
#9, 11
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