Beginning Algebra, 11th Edition

7.1

rational expression
lowest terms

7.3

least common

denominator (LCD)

7.5

complex fraction

7.6

proposed solution

extraneous solution (value)

7.8

direct variation

constant of variation

inverse variation

KEY TERMS

SUMMARY

CHAPTER 7

1.A rational expressionis
A.an algebraic expression made up
of a term or the sum of a finite
number of terms with real
coefficients and whole number
exponents
B.a polynomial equation of
degree 2
C.an expression with one or more
fractions in the numerator, or
denominator, or both
D.the quotient of two polynomials
with denominator not 0.

2.A complex fractionis

A.an algebraic expression made up

of a term or the sum of a finite

number of terms with real

coefficients and whole number

exponents

B.a polynomial equation of degree 2

C.a quotient with one or more

fractions in the numerator, or

denominator, or both

D.the quotient of two polynomials

with denominator not 0.

3.If two positive quantities xand yare

in direct variation,and the constant

of variation is positive, then

A.as xincreases, ydecreases

B.as xincreases, yincreases

C.as xincreases, yremains constant

D.as xdecreases, yremains constant.

4.If two positive quantities xand yare

in inverse variation,and the constant

of variation is positive, then

A.as xincreases, ydecreases

B.as xincreases, yincreases

C.as xincreases, yremains constant

D.as xdecreases, yremains constant.

TEST YOUR WORD POWER

See how well you have learned the vocabulary in this chapter.

ANSWERS

1.D; Examples: 2.C; Examples: , ,

3.B; Example:The equation represents direct variation. When If xincreases to 3, then yincreases to

4.A; Example:The equation y=x^3 represents inverse variation. When x=1, y=3.If xincreases to 2, then ydecreases to , or 23 1 21.

y= 3 x x=2, y=6. 3132 =9.

2

a+ 1

a^2 - 1

x-^1 y

x+^1 y

2

3

4

7

• 3
  4 y
  ,
  5 x^3
  x+ 2
  ,
  a+ 3
  a^2 - 4 a- 5

7.1 The Fundamental Property of Rational

Expressions

To find the value(s) for which a rational expression is
undefined, set the denominator equal to 0 and solve the
equation.

Find the values for which the expression is undefined.

Factor.

or Zero-factor property

or Solve for x.

The rational expression is undefined for 4 and so and

xZ-4.

• 4, xZ 4

x= 4 x=- 4

x- 4 = 0 x+ 4 = 0

1 x- 421 x+ 42 = 0

x^2 - 16 = 0

x- 4

x^2 - 16

QUICK REVIEW

CONCEPTS EXAMPLES

(continued)

CHAPTER 7 Summary 483