Name ___________________________________________

Math 3 Unit 7: Rationals

April 23

● Simplify rational expressions

HW: worksheet 7.1

April 24

● Multiply and divide rational expressions

HW: worksheet 7.2

April 25

● Add and subtract rational expressions with common denominators

HW: worksheet 7.3

April 26

● Add and subtract rational expressions

HW: worksheet 7.4

April 27

● QUIZ!!● Solve rational

equations

HW: worksheet 7.5

April 30

● Solve rational expressions

HW: worksheet 7.6

May 1

● Asymptotes and holes of rational functions

HW: worksheet 7.7

May 2

● Graph rational functions

HW: worksheet 7.8

May 3

● Review for test

HW: finish review

May 4

● TEST!!!

7.8 - Graph Rational FunctionsFor each rational function, determine the holes, vertical asymptotes, domain, and horizontal asymptote. Then graph the rational function.

1. f (x)= 4x−5

2.

f (x)= x−1x2+3 x−4

Holes: _______________________ Holes: _______________________

VA: _________________________ VA: _________________________

Domain: _____________________ Domain: _____________________

HA: _________________________ HA: _________________________

3. f (x)= 2

x2+3 x−10

4.

f (x)= x2−4 x+3x2−x−6

Holes: _______________________ Holes: _______________________

VA: _________________________ VA: _________________________

Domain: _____________________ Domain: _____________________

HA: _________________________ HA: _________________________

7.1 - Simplifying Rational ExpressionsSimplify each rational expression.

1. 27

27 x+18 2. v2−7 v−30v2−5 v−24

3. x2+8x+12x2+3 x−18

4. b2+3b−28b2−49

5. 4 n−46n−20 6. 2v

2+10 v−488v+64

7. 6v3+42v2

2v2+26v+848. x

3− x2−42 x2x2−20 x+42

9. 9x2+81 x

x3+8 x2−9 x

7.2 - Multiply and Divide Rational ExpressionsSimplify each rational expression.

1. k+9

(k−8 ) (k−7 )⋅ (k−7 ) ( k+1 )

k+1 2. 9 (m+7 )

(m+4 ) (m+7 )÷ 98 (m+4 )

3. 6 (r+7 )2r

⋅ 2010 (r+7 )

4. a2−9a+20a2−16

⋅ a2+5a+42a−10

5. x2+5 x−362 x−6

÷ (x−4 ) 6. 6n+2414n−4

÷ 8n+3214n−4

7. x2−15 x+54x2−14 x+48

÷ 1x−8

8. (b+6 )⋅ 10b2b+12 9. 3x−9

x−6÷ x

2−11 x+24x2−36

7.7 - Asymptotes and Holes of Rational FunctionsFor each rational function, determine the holes, vertical asymptotes, domain, and horizontal asymptote.

Holes: Vertical Asymptotes:

Domain: Horizontal Asymptote:

1. f ( x )=5 ( x−3 ) ( x+3 )6 ( x+3 ) ( x−6 )

2. f (x)=6 (x−1)( x+9)(x−8)(x+7)

(x+9)(x+7)(x−3)

3. f ( x )= 2 ( x+3 ) ( x+4 )7 x (3 x+7 ) ( x−3 )

4. f (x)=3 x−12x2−2 x−8

5. f (x)=−4 x+16x−4

6. f (x)= x+22 x+6

7. f (x)= x3−9 x3 x2−6 x−9

8. f (x)=x−4x2−4

7.6 - Solve Rational Equations with Extraneous SolutionsSolve for the variable.

1. 32x

− 53x

=2 2. 12= 1x+3

+ 1x

3. 3x= 12x+7 4.

2y+ 12= 52 y

4. 106 x+7

= 62 x+9 5.

2x+2

−1x= −4x2+2x

7. 3x+5

+ 2x−5

= −4x2−25 8.

102 y+8

− 7 y+8y2−16

= −82 y−8

7.3 - Add and Subtract Rational Expressions with Common DenominatorsSimplify each rational expression.

1. 915x

+ 215 x 2.

78a

− 38a 3.

25x+9

+ x+35x+9

4. p−13 p+4

+ 2 p+93 p+4 5.

7 x+4x2+3 x+2

− 3 x−2x2+3 x+2

6. x

x2−25− 5x2−25

7. m−3n6m3n

−m+3n6m3n

8. u−v8v

−6u−3v8 v 9.

2 r+63 r−6

+ r+33 r−6

10. x−43

+ 5 x3 11.

5a2+3a+2

+ 6a+1a2+3a+2

12. x+2

2x2+13 x+20− x+32 x2+13 x+20

7.4 - Add and Subtract Rational ExpressionsSimplify each rational expression.

1. 6

x2+11 x+30− 7 xx+5 2.

5 xy2 z2

− 4y3 z5

3. 5h+3

+ 5h2−9

4. x+2

x2−10 x+16+ x−3x−8 5.

4 xx+6

− 9x−6 6. r

3−48 r s2

− r2+712r3

7. 3x+7

+ 4x−8 8.

x+4x2+2 x−15

+ x−2x2−2 x−3

9. x+7

x2+x−56− x+8x2−49

7.5 - Solve Rational EquationsSolve for the variable.

1. 3x−7

= 24 x+1 2.

7x+1

= 6x−5

3. 7x−3

=4x 4.

4x−5

= 2x+8

5. x−37

=52 6.

3x+4

= x−416

7. x

x+24=2x 8.

x+3x+1

= 15x+7