When we add or subtract rational expressions, we must first have a common denominator. Once we have a common denominator, we add or subtract numerators and place the result over the common denominator. Lastly, we always simplify our result.
Test Objectives:•Demonstrate the ability to find the LCD for a group of rational expressions
•Demonstrate the ability to add rational expressions
•Demonstrate the ability to subtract rational expressions
Adding & Subtracting Rational Expressions Test:
#1:
Instructions: Perform each indicated operation.
a)
v - 3 | - | v + 1 |
3(5v - 2) | 3(5v - 2) |
b)
x + 1 | + | x + 3 |
(x + 2)(x + 7) | (x + 2)(x + 7) |
#2:
Instructions: Perform each indicated operation.
a)
p - 4 | + | 2p - 3 |
2(2p + 5) | 2(2p + 5) |
b)
6n + 5 | - | n + 3 |
(3n - 1)(5n + 2) | (3n - 1)(5n + 2) |
#3:
Instructions: Perform each indicated operation.
a)
4n | - | 2n - 1 |
n - 2 | 4n - 8 |
b)
5 | + | 4 |
2m + 3 | 5m + 4 |
#4:
Instructions: Perform each indicated operation.
a)
3x^{2} - 5x - 7 | + | 4x^{2} - 3x + 8 |
2x^{2} - 2 | 5x + 5 |
#5:
Instructions: Perform each indicated operation.
a)
7x | - | 3x | + | 2x - 5 |
x^{2} + 3x | x^{2} - x | x^{2} + 2x - 3 |
Written Solutions:
Solution:
a)
-4 |
3(5v - 2) |
b)
2 |
x + 7 |
Solution:
a)
3p - 7 |
2(2p + 5) |
b)
1 |
3n - 1 |
Solution:
a)
14n + 1 |
4(n - 2) |
b)
33m + 32 |
(2m + 3)(5m + 4) |
Solution:
a)
8x^{3} + x^{2} - 3x - 51 |
10(x + 1)(x - 1) |
Solution:
a)
3(2x - 7) |
(x + 3)(x - 1) |