Applications of Rational
Expressions
Find value of a variable
In physics, the focal length, f, of a lens is
given by: 1 1
1
f
=
p
+
q
In the formula, p is the distance from the
object to the lens and q is the distance from
the lens to the image.
If a lens
College Algebra
Chapter 8
Section 2
If n is any positive integer, then
a
1
n
=a
n
Assuming that the nth root of a is a real number.
Examples:
8
4
1
3
= 8=2
3
xy = ( xy )
1
4
Evaluate:
1
81 = 81 = 3
4
4
( 27 x )
6
1
3
= 27 x = 27 x = 3 x
3
6
3
3
6
2
If m a
College Algebra
Chapter 8 Section 1
nth Roots
If a = bn
b is the nth root of a
Example: a = b4 would mean that b is the fourth
root of a.
A third root is called a cube root.
A second root is called a square root.
Even Roots
a = bn
If n is a positiv
COLLEGE ALGEBRA
MATH 151
a
n
1
=n
a
1
1
2 = 3=
2
8
3
a =1
0
3 =1
0
n
a
n
1
1
1
n
= = n and n = a
a
a
a
3
1
1
2 = = 3
2
2
3
1
= 46
6
4
a a = a
m
n
m+n
2 2 = 2
5
3
5+ 3
m
a
mn
=a
n
a
6
4
6 3
3
=4 =4
3
4
(a )
mn
(6 )
53
=a
=6
53
m n
=6
15
( ab )
n
( 6x )
3
=
College Algebra
Chapter 10 Review
Name:_
Find each of the following for f(x) = x-4 and g(x) = 2x-3
1. (f-g)(x)
2. (f g)(x)
-x-1
3. (fg)(x)
2x2 11x + 12
2x 7
Determine whether each given value of x is a zero of the given function.
4. x = 5, p(x) = x 5
NO
5
College Algebra
Chapter 9.4
Solve the following for v
kFr
w= 2
v
kFr 2
wg = 2 g
v
v
v
wv 2 kFr
=
w
w
2
v
2
kFr
kFr
kFr w
kFrw
=
=
=
g
=
w
w
w
w
w
Solve the following for A
d=
4A
d
A=
4
2
Solve the following for: t
s = 2t + kt
2
0 = 2t + kt s
2
k ) k 4 (
College Algebra
ReviewChapter 9
Name_
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Solve the equation by completing the square.
1) 15d2 + 28d + 12 = 0
1)
Use the quadratic formula to solve the equation
College Algebra
Chapter 7 Test Review
Name:_
1. Find all numbers that are not in the domain of the function. Then give the domain using
set notation.
2. Express the rational expression in lowest terms.
Perform the indicated operation and express in lowest
Chapter 8.6
Odd-Root Property
If n is an odd positive integer,
x =k
n
is equivalent to
x= k
n
Solve
x = 27 x = 27 x = 3
3
( x 2)
3
3
= 24 x 2 = 24 x = 2 + 2 3
3
3
Even Root Property
Suppose n is a positive even integer
If k > 0, then xn = k is equivale