Pre-Calculus 11 Ch 1 Radicals
1.5 Multiplying and Dividing Radical Expressions (Part 2 - Rationalizing)
We do not like having radicals in the denominators of an expression. Therefore we rewrite it
without. This process is called rationalizing the denomina
Pre-Calculus 11 Ch2 Rational Expressions
2.3 Sums and Differences of Rational Expressions
Review: Simplify
y
3
state any restrictions on the expression
y 9 y 3
2
Recall the mathematical F wordFRACTIONS
3 2
+ =
7 7
3 y 11 y
+
=
2x 2x
They gotta be COMMOM D
Pre-Calculus 11 Ch2 Rational Expressions
2.2 Multiplication and Division of Rational Expressions
Review: Simplify
3 x 2 10 x 8
, and state any restriction(s) on the expression.
x 2 16
Multiplying Rational Expression:
Just like multiplying two integer rat
Pre-Calculus 11 Ch2 Rational Expressions
2.4 Mixed Operations Part 2
Review: Different ways of showing division
125 5 same as
( x 2)
125
; ( x 2 ) ( x 2 + 3) same as 2
5
( x + 3)
1
1 2
1 3
same as 2 now that is a fraction! But remember this is the same a
Pre-Calculus 11 Ch 1 Radicals
1.6 Radical Equations
Review: Factor fully: 1) x 2 + 5x + 6
2) 3x 2 + 8x + 4
Restrictions:
Remember:
There are restrictions on x
And x implies only the positive root of x.
Ex: 1) Find the restrictions on the following:
a)
x
Pre-Calculus 11 Ch 1 Radicals
1.2 Radical operations
Name:
Review:
n
x
m
n
x =
xm =
n
x
=
y
Remember:
x is
Positive or Positive/Negative Root?
Solve: x 2 = 16
x = 2,
x = 2,
x 2 = 2,
Ex: 1) Solve.
a) x 2 = 64
Solve:
b) x 4 = 81
16 =
c) x 3 = 125
d) x 2 =
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Pre-Calculus 11 Ch2 Rational Expressions
2.1 Properties of Rational Expressions
Rational Expression:
Domain:
Undefined Values:
Factoring Reminders: common factor, difference of squares,
Pre-Calculus 11 Ch 1 Radicals
1.4 Simplifying Radicals
What do you think?
Name:
2 x + 3 x = _ so, 2 5 + 3 5 = _
Therefore
Ex: 1) Simplify.
a) 6 2 4 2 + 2
b) 3 3 5 + 2 3 5 4 3 5
Sometimes you may have to simplify the radical first.
Ex: 2) Simplify.
a) 18 8