Page 285 - Algebra 1

L E S S O N Simplifying Rational Expressions 43
Warm Up
1. Vocabulary The largest whole number that is a factor of two or more
(SB 9)
indicated numbers is the __________.
Simplify.
2. 36 3. 32x 4. 7x-49x
__5_2 (SB9) 48 (32) 48x7 (38) 7x
5. Factor 3x2 + 6x3 completely. (38)
New Concepts Rational expressions are fractions with a variable in the denominator. Since division by 0 in mathematics is undefined, the denominator of a rational
expression must not equal 0.
Determining When an Expression is Undefined
Determine the values for which each rational expression is undefined. a. _x+8
Example
1
Caution
Some students may mistakenly think that if the numerator equals zero, the fraction is undefined. Remind them that dividing zero by a nonzero number always results in a quotient equal to zero.
4x SOLUTION
denominator = 4x 4x = 0 when x = 0
b. _2x+1 x-4
SOLUTION
denominator = x - 4 x - 4 = 0 when x = 4
Start with the denominator.
The expression is undefined at x = 0.
Start with the denominator.
The expression is undefined at x = 4.
Start with the denominator.
Find its zero value.
Divide by 3.
The expression is undefined at x = -7.
(x + 5)(x - 3) __
3x + 21 SOLUTION
denominator = 3x + 21 3x + 21 = 0
x + 7 = 0 x = -7
c.
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