Math Practice: Rational Equations

18 Math 070 Chapter 7 Rational Expressions and Equations (7.1)

Sec. 7.1

Simplifying Rational Expressions

To reduce an algebraic fraction: factor first, then cancel _____________________________. 1.
4w3 28w 2

2.

27 a  3 33

3.

y 2  7 y  18 y2  6y  8

19 Math 070 Chapter 7 Rational Expressions and Equations (7.2)

Sec. 7.2

Multiplying and Dividing Rational Expressions

To multiply algebraic fractions: factor first, next cancel __________________________ and then multiply across. 4. y2  9y  8 y4  2 y2 1 y  4 y  32

5.

x 3  27 x 2  6 x  9  x 2  9 x 2  3x  9

6.

3x 2  9 x  30 5 x  5  x2  1 15 x  30

20 Math 070 Chapter 7 Rational Expressions and Equations (7.2)

To divide algebraic fractions: factor first, then flip over the second fraction; ___________________ & multiply across. 7.
4 x 2  25 2 x  5  x 3 x2  9

8.

y2  9 y  3  6 y  12 y  2

9.

a 3  2a 2 a 2  6 a  5  2 a2  4 a  3a  10

21 Math 070 Chapter 7 Rational Expressions and Equations (7.3-7.4)

Sec.7.3-7.4 Adding & Subtracting Rational Expressions Add or subtract, as indicated: 1.
5 2  2 8a a

Steps: #1: #2: #3: #4: Find the least common Denominator Build equivalent fractions Add or subtract numerators (simplify) Reduce, if possible

2.

4 3  2 7 a 3 2a

22 Math 070 Chapter 7 Rational Expressions and Equations (7.3-7.4)

4.

5 7  x3 x

5.

7 2  3y 1 3y

6.

4 2  5y  5 3y  3

Hint: Factor denom. 1st

23 Math 070 Chapter 7 Rational Expressions and Equations (7.3-7.4)

7.

1 2  3x  3 4 x  4

8.

5 4  2 x  9 x  7 x  12
2

9.

5a 1  3a  4 4  3a

24 Math 070 Chapter 7 Rational Expressions and Equations (7.3-7.4)

10.

1 1 2p   2 p2 p2 p 4

11.

1 1 5   2 w  1 w  4 w  3w  4

25 Math 070 Chapter 7 Rational Expressions and Equations (7.5)

Sec. 7.5

Complex Rational Expressions

Strategy: