algebra 2: rational expressions, equations, and …...algebra 2: rational expressions, equations,...
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Algebra 2: Rational Expressions, Equations, and Functions
Topic F3: Addition of Rational Expressions | VERSION A
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Name: _______________________________________________
Combine the following rational expressions. Reduce all answers to lowest terms.
1. !
!!!+
!!!!
=
2. !
!!!+
!!!!
=
3. !
!!!+
!!!!
=
Combine the following fractions:
4. !!+!!=
5. !!"
+!!=
6. !!+
!!"=
7. !!"
+!!=
Combine the following rational expressions.
8. !
!!!!+
!!!!"!"!!!!
=
9. !!!!!
+!!!!!!!!!!
=
10. !!!!!
+!!!!!!!!!
=
Algebra 2: Rational Expressions, Equations, and Functions
Topic F3: Addition of Rational Expressions | VERSION A
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Name: _______________________________________________
11. !
!!!!+
!!!"!!!!"!!!
=
12. !
!!!!!!+
!!!!!!!!
=
13. !!!!!!!!"
+!
!!!!!!!=
14. !!!!!!!!
+!
!!!!!!=
15. !!!!!!!!!!!
+!!!
!!!!!!!!=
16. 3 + 43𝑥+3 =
17. 2 + 35−𝑡 =
18. Let 𝑓 𝑥 = 2𝑥−4 and 𝑔 𝑥 = 𝑥+3
𝑥2−𝑥−12, find
𝑓 𝑥 + 𝑔 𝑥 =
19. Let 𝑓 𝑥 = 3𝑥𝑥2+5𝑥+4 and 𝑔 𝑥 = 1
𝑥2+7𝑥+12, find
𝑓 𝑥 + 𝑔 𝑥 =
20. The formula 𝑃 = 1𝑎 +
1𝑏 is used by optometrists to
help determine how strong to make the lenses for a pair of eyeglasses. If 𝑎 is 15 and 𝑏 is 0.25, find the corresponding value of 𝑃.
Algebra 2: Rational Expressions, Equations, and Functions
Topic F3: Addition of Rational Expressions | VERSION A
www.varsitylearning.com 3
Name: _______________________________________________
Combine the following rational expressions. Reduce all answers to lowest terms.
1. 3𝑥+3 +𝑥
𝑥+3 = 1
2. !
!!!+
!!!!
= 1
3. !
!!!+
!!!!
= 1
Combine the following fractions:
4. !!+!!= !
!
5. !!"
+!!= !
!"
6. !!+
!!"= !"
!"
7. !!"
+!!= !"
!"
Combine the following rational expressions.
8. !
!!!!+
!!!!"!"!!!!
= !!!!!
9. !!!!!
+!!!!!!!!!!
= !!!!!
10. !!!!!
+!!!!!!!!!
= !!!!!
Algebra 2: Rational Expressions, Equations, and Functions
Topic F3: Addition of Rational Expressions | VERSION A
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Name: _______________________________________________
11. !
!!!!+
!!!"!!!!"!!!
= !
!!!!
12. !
!!!!!!+
!!!!!!!!
= !
(!!!)(!!!)
13. !!!!!!!!"
+!
!!!!!!!=
!!!! !!!
14. !!!!!!!!
+!
!!!!!!=
!!!! !!!
15. !!!!!!!!!!!
+!!!
!!!!!!!!=
!!!!!! !!!
16. 3 + 43𝑥+3 =
!!!!"!!!!
17. 2 + 35−𝑡 =
!"!!!!!!
18. Let 𝑓 𝑥 = 2𝑥−4 and 𝑔 𝑥 = 𝑥+3
𝑥2−𝑥−12, find
𝑓 𝑥 + 𝑔 𝑥 = !
!!!
19. Let 𝑓 𝑥 = 3𝑥𝑥2+5𝑥+4 and 𝑔 𝑥 = 1
𝑥2+7𝑥+12, find
𝑓 𝑥 + 𝑔 𝑥 = !!!!!"!!!
!!! !!! !!!
20. The formula 𝑃 = 1𝑎 +
1𝑏 is used by optometrists to
help determine how strong to make the lenses for a pair of eyeglasses. If 𝑎 is 15 and 𝑏 is 0.25, find the
corresponding value of 𝑃. !"!"