Page 339 - Algebra 1

Example
3
Simplifying Expressions with Integer Exponents
Simplify each rational expression, if possible. __
a. b-2b a3 a3
SOLUTION
b - 2b __
a3 a3 = -_b
The expressions have like denominators. Subtract the numerators.
Write the expression with only positive exponents.
The expressions have like denominators. Subtract the numerators.
3 a_
b. pq-2 - 7 p-1q2
SOLUTION
_ pq-2 - 7p
Hint
pq-2 is the same as _p . q2
q2 = p - 7p
__ q2 q2
_ = - 6p
q2
Application: F_encing a Field
_
6a km
Example
4
A rectangular field ha_s length 6a
8 3a + 4
kilometers and width 3a + 4 kilometers. _
3a + 4
Find the amount of fencing needed to enclose all four sides.
8 km 3a + 4
SOLUTION
P = 2(l + w)
6a 8
Write the formula for the perimeter of a rectangle. Substitute for the length and width.
The expressions have like denominators. Add the numerators.
Factorthenumerator.TheGCFis2. Simplify.
__
P = 2(_ + )
3a + 4 3a + 4 = 2(6a + 8 )
3a + 4 _1
=2 2(3a+4) (3a+4 )
324 Saxon Algebra 1
= 2(2)
1
=4
4 kilometers of fencing is needed.