Page 338 - Algebra 1

Example
2
Simplifying Rational Expressions
Simplify each rational expression, if possible. Identify any excluded values.
_2 a. 8h 12h
SOLUTION
12h = 0 h=0 h≠0
_2 8h
Set the denominator equal to zero. Solve.
0 is the excluded value.
Factor out the GCF. Simplify.
Set the denominator equal to zero. Solve.
3 is the excluded value.
Factor the numerator. Divide out common factors. Simplify.
Set the denominator equal to zero. Solve.
-2 is the excluded value.
Factor the numerator. Divide out common factors. Simplify.
12h _1
= 4h(2h) 4h(3)
1
= 2h _
3
b. _2m-6
m-3 SOLUTION
m-3=0 m=3 _m≠3
2m - 6 _m - 3
1
2 (m - 3)
(m - 3) 1
y+2=0
y = -2
_y ≠ -2 4y2 + 8y
y_ 4y(y + 2)
= (y+2) 1
= 4y
=2 c.
_2
4y +8y
Hint
If there is more than one term in the numerator or denominator, begin by factoring.
y + 2 cannot be factored. 4y2 + 8y can be factored.
y+2 SOLUTION
+2
1
Lesson 51 323