Beginning Algebra, 11th Edition

SUMMARY EXERCISES on Rational Expressions and Equations

Write a mathematical expression for each exercise. See Section 2.7.

97.Andrew drives from Pittsburgh to Philadelphia, a distance of 288 mi, in thours. Find his

rate in miles per hour.

98.Tyler drives for 20 hr, traveling from City Ato City B, a distance of dkilometers. Find

his rate in kilometers per hour.

99.Jack flies his small plane from St. Louis to Chicago, a distance of 289 mi, at zmiles per

hour. Find his time in hours.

100.Joshua can do a job in rhours. What portion of the job is done in 1 hr?

PREVIEW EXERCISES

Students often confuse simplifying expressionswith solving equations.We re-

view the four operations to simplify the rational expressions and as follows.

Add:

Write with a common denominator.

Add numerators.

Keep the same denominator.

Combine like terms.

Subtract:

Write with a common denominator.

Subtract numerators.

Keep the same denominator.

Combine like terms.

Multiply:

Multiply numerators and multiply

denominators.

Divide:

Multiply by the reciprocal of the

divisor.

Multiply numerators and multiply

= denominators.

x- 2

x

=

1

x

#x-^2

1

1

x

,

1

x- 2

=

1

x 1 x- 22

1

x

#^1

x- 2

=

- 2

x 1 x- 22

=

x- 2 - x

x 1 x- 22

=

11 x- 22

x 1 x- 22

-

x 112

x 1 x- 22

1

x

-

1

x- 2

=

2 x- 2

x 1 x- 22

=

x- 2 +x

x 1 x- 22

=

11 x- 22

x 1 x- 22

+

x 112

x 1 x- 22

1

x

+

1

x- 2

1

x- 2

1

x

(continued)

7.2 Multiplying and Dividing Rational Expressions