Polynomial Fractions
Provided by the Academic Center for Excellence 1 Reviewed June 2008
Polynomial Fractions
You can navigate to specific sections of this handout by clicking the links below.
Simplifying: pg. 1
Multiplying: pg. 2
Dividing: pg. 2
Adding/Subtracting: pg. 2
Complex Fractions: pg. 3
Sample Problems: pg. 4
Simplifying
To simplify a polynomial faction, start by factoring both the numerators and denominators
completely. See our factoring handout if you need review on factoring methods. Next
cancel out any common factors.
Example 1:
80
2
+ 80
30 + 30
→
80 ( + 1 )
30 ( + 1 )
→
2 ∙ 2 ∙ 2 ∙ 2 ∙ 5 ∙ ∙ ( + 1 )
2 ∙ 3 ∙ 5 ∙ ( + 1 )
2 ∙ 2 ∙ 2 ∙ 2 ∙ 5 ∙ ∙ ( + 1 )
2 ∙ 3 ∙ 5 ∙ ( + 1 )
→
Example 2:
Polynomial Fractions
Provided by the Academic Center for Excellence 2 Reviewed June 2008
Multiplying
To multiply polynomials, first factor both the numerator and denominator of both
fractions. Second, combine the two fractions together. Third, cancel out like terms.
Example 3:
Factor Multiply
Cancel
Example 4:
Factor Cancel
Dividing
When dividing polynomial fractions, first flip the second fraction and then multiply.
See previous page for examples on multiplying.
Example 5:
Flip the second term Factor Multiply
Cancel
Adding/Subtracting
When adding and/or subtracting polynomial fractions, first get common denominators,
then add and/or subtract the numerators together. Finally, simplify.
Example 6:
Get common denominators Add Simplify
Provided by the Academic Center for Excellence 3 Polynomial Fractions
Example 7:
Complex Fractions
To solve a complex fraction, first find the common denominator for the entire fraction.
Then change each term’s denominator to this common denominator. Once all the terms
have the same denominator, the denominators can be removed.
Example 8:
Example 9:
Provided by the Academic Center for Excellence 4 Polynomial Fractions
Sample Problems
Write each fraction in lowest terms.
1.
90d
2
2.
25k
5
3.
-6k
6
80d
3
30k
3
-11k
4.
72h
3
5.
54k
2
6.
-20i
2
+ 200i
81h
5
18k
-45i
2
+ 475i - 250
7.
63h
3
8.
27g
4
9.
8b
2
+ 6bw + w
2
45h
2
45g
5
24b
2
+ 54bw + 12w
2
Write each product in lowest terms.
10.
2k
2
+ 3k
*
12v
2
- 28v
11.
15q
2
- 9q
*
7g
12.
25g + 50
*
g
6k
3
+ 9k
2
4v
3q
14g
3
g + 2
25(g - 2)
Complete and write in lowest terms.
13.
5k
+
4k
14.
8b
+
9b
15.
7f
+
5f
15
5
12
6
15
5
16.
9e
-
8e
17.
5j
-
7j
18.
5k - 9
-
3k
7
21
7
21
4
8
19.
7d
-
8d
20.
5i
-
3i
21.
3a + 4
+
4a - 14
7
14
16
8
6
3
22.
6e
+
8e - 14
23.
8
+
9
24.
7j + 7
+
6
5
20
r
f
6j
2u
25.
9a
-
6a
26.
4
-
6
27.
4t + 5
-
-8t + 2
7
28
d
y
2b
16b
28.
6
-
3
29.
5d
-
8d - 7
30.
2
+
4
b
r
7
28
v
a
Provided by the Academic Center for Excellence 5 Polynomial Fractions
Simplify
31.
32.
33.
34.
35.
36.
37.
38.
39.
40.
41.
4
2.
43.
44.
45.
46.
47.
48.
49.
50.
51.
52.
Provided by the Academic Center for Excellence 6 Polynomial Fractions
Solutions
1. 9
8d
2. 5k
2
6
3. 6k
5
11
4. 8
9h
2
5. 3k
6. 4i
9i-5
7. 7h
5
8. 3
5g
9. 2b+w
6(b+2w)
10. 3v-7k
3k
11. 5q-3
2g
2
12. g
g-2
13. 17k
15
14. 13b
6
15. 22f
15
16. 19e
21
17. 8j
21
18. 7k-18
8
19. 3d
7
20. 11i
16
21. 11a-24
6
22. 16e-7
10
23. 8f+9r
rf
24. 7ju+7u+18j
6ju
25. 15a
14
26. 2(2y-3d)
dy
27. 20t+19
8b
28. 3(2r-b)
br
29. 12d+7
28
30. 2(a+2v)
va
Provided by the Academic Center for Excellence 7 Polynomial Fractions
31.
32.
33.
34.
35.
36.
37.
38.
m + n
39.
40.
-a
41.
42.
x + y
43.
44.
45.
1
46.
1
47.
-1
48.
49.
50.
51.
52.
