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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