Name:_______________ Date:_______________
5.0 Worksheet (2 pages) Simplify the following Rational Expressionsβ¦.make sure answers are in FACTORED FORM.
1. ππ(π+π)
πππ 2.
(π+π)(πβπ)
π+π 3.
πβπ
πβπ
4. π+π
π+π 5.
ππ(ππβπ)
ππ(ππβπ) 6.
π(πβπ)
ππ
7. π(πβπ)
ππ+π 8.
βπππππ(πβπ)
ππππ(πβπ) 9.
ππβπ
ππβππ+π
10. πππ+ππ+π
πππβππβπ 11.
ππβππ
πβπ 12.
πππ+ππβπ
ππβπβπ
Name:_______________ Date:_______________
Multiplying and Dividing Rational Expressionsβ¦make sure answers are in FACTORED FORM.
13. πππππ
πππβπππ
πππ 14.
πβπ
πβπβππβπ
πβπ 15.
ππβππ
ππ+πβ
π+π
ππ+ππ+ππ
16. ππβππ+π
πβ
π
(πβπ)π 17.
ππππ
πππβππππ
πππ 18.
ππππ
πβ
π
ππππ
19. ππβππ
ππβππΓ·
π+π
πβπ 20.
πππβπππ
πππ+ππβπΓ·
πππ
πππβπ 21.
ππβππ+π
πΓ·
πβπ
ππ
22. ππ+π
ππ+ππΓ·
ππβπ
ππβπ 23.
ππβππ
ππ+πΓ·
ππβππβπ
ππβπβπ 24.
ππ β ππ
ππ + ππβππ + ππ + π
ππ β ππΓ·
π + π
ππ + ππ
Name:_______________ Date:_______________
5.1 Worksheet (2 pages) Find the SUM or DIFFERENCE.
a. π₯2+3π₯
π₯+2+
2π₯+6
π₯+2 b.
7π₯+3
π₯2β1β
6
π₯β1
c. 7π₯+3
π₯2β1β
6π₯+4
π₯2β1
d. 6π¦+13
π¦2β4π¦β21β
π¦β2
π¦2β4π¦β21
e. 4π₯
π₯2+9π₯+18+
5
π₯+6
f. 3π+6
π2β16β
7
6π+24
Name:_______________ Date:_______________
Simplify Each Complex Fraction.
g.
1
π¦2β1
1+1
π¦
h. 25
πβπ
5+π
i. 4+
12
2π₯β3
5+15
2π₯β3
j. π₯
3π₯β2π₯
9π₯2β4
Name:_______________ Date:_______________
5.2 Worksheet (2 pages) Solve each Rational Equation. Make sure to include all restrictions on Domain and
Check solutions for any extraneous solutions.
1. 1
6π2=
1
3π2β
1
π 2.
π+6
4π2+
3
2π2=
π+4
2π2 3.
1
π₯=
6
5π₯+ 1
4. 1
π£+
3π£+12
π£2β5π£=
7π£β56
π£2β5π£ 5.
1
π2βπ+
1
π=
5
π2βπ 6.
1
πβ8β 1 =
7
πβ8
7. 1
πβ2+
1
π2β7π+10=
6
πβ2 8. 1 =
π£+2
π£β4+
7π£β42
π£β4 9.
πβ4
5π=
1
5π+ 1
Name:_______________ Date:_______________
10. 1 +π₯2β5π₯β24
3π₯=
π₯β6
3π₯
11. 1 =1
π₯2+2π₯+
π₯β1
π₯
12. π+5
π+8= 1 +
6
π+1 13.
π+5
π2β2πβ 1 =
1
π2β2π
14. πβ2
π+3β 1 =
3
π+2 15.
5
π3+2π2=
4
π+2+
1
π2
Name:_______________ Date:_______________
5.3 Worksheet (2 pages) Given the following Rational Functions. Identify the asymptotes, domain, and range of each function.
a) π(π) =π
π+π b) π(π) =
π
πβ π
c) π(π) =π
π+πβ π d) π(π) =
βπ
πβπ+ π
e) π(π) =π
π f) π(π) =
βπ
πβπ+ π
g) π(π) =π
ππβπ h) π(π) =
π
ππ+πβ π
Name:_______________ Date:_______________
Graph each function. State the Domain and Range.
i) π(π) =π
πβπβ π
j) π(π) =βπ
π+πβ π
k) π(π) =π
πβ π
l) π(π) =βπ
π
ππβπ
+ π
Name:_______________ Date:_______________
5.4 Worksheet (1 page) For the following Functions, find (if they apply to the function):
a) the vertical asymptote(s)
b) the horiztonal/slant asymptotes
c) the holes
1. π(π₯) =2π₯
π₯2β1 2. π(π₯) =
π₯2β5π₯+6
π₯2β4π₯+3
3. π(π₯) =8
π₯2βπ₯β6 4. π(π₯) =
π₯2+11π₯+18
2π₯+1
5. β(π₯) =π₯2β9
2π₯2+1 6. π(π₯) =
π₯β4
π₯2β3π₯
Name:_______________ Date:_______________
5.5 Worksheet (2 pages) For the following Functions, find (if they apply to the function):
a) the π-intercepts, and π-intercepts
b) the vertical asymptote(s)
c) the horiztonal/slant asymptotes
d) the holes
e) any additional points needed
f) then, graph each function
7. π(π₯) =2π₯
π₯2β1
8. π(π₯) =π₯2β5π₯+6
π₯2β4π₯+3
Name:_______________ Date:_______________
9. π(π₯) =8
π₯2βπ₯β6
10. π(π₯) =π₯2+11π₯+18
2π₯+1
11. β(π₯) =π₯2β9
2π₯2+1
12. π(π₯) =π₯β4
π₯2β3π₯
Name:_______________ Date:_______________
5.6 Worksheet (2 pages) Solve Each Rational Inequality. Write answers in interval notation.
1. 3 β4
π₯>
5
4π₯ 2.
5
3πβ
3
4π>
5
6
3. π₯β2
π₯+2+
1
π₯β2>
π₯β4
π₯β2 4.
3
4β
1
π₯β3>
π₯
π₯+4
Top Related