Adding Subtracting Rational Expressions.pdf, Study notes of Algebra

28) Split into a sum of two rational expressions with unlike denominators: 2x + 3 x. 2 + 3x + 2. -2-. Page 3. Kuta Software - Infinite Algebra 2.

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Kuta Software - Infinite Algebra 2 Name___________________________________
Period____Date________________
Adding/Subtracting Rational Expressions
Simplify each expression.
1)
u
v
8
v
+
6
u
− 3
v
8
v
2)
m
− 3
n
6
m
3
n
m
+ 3
n
6
m
3
n
3)
5
a
2
+ 3
a
+ 2
+
5
a
+ 1
a
2
+ 3
a
+ 2 4)
5
10
n
2
+ 16
n
+ 6
+
n
− 6
10
n
2
+ 16
n
+ 6
5)
r
+ 6
3
r
− 6
+
r
+ 1
3
r
− 6 6)
x
+ 2
2
x
2
+ 13
x
+ 20
x
+ 3
2
x
2
+ 13
x
+ 20
7)
6
x
− 1
5
x
48)
6 −
x
+ 5
(
7
x
− 5
)(
x
+ 4
)
9)
3
x
+ 7
+
4
x
− 8 10)
3
4
v
2
+ 4
v
7
2
11)
7
3
8
12
x
− 8 12)
5
n
+ 5
+
4
n
2
n
+ 6
13)
2
x
5
x
+ 4
+
6
x
2
x
+ 3 14)
2
3
x
2
+ 12
x
+
8
2
x
-1-
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Kuta Software - Infinite Algebra 2 Name___________________________________

Adding/Subtracting Rational Expressions Date________________ Period____

Simplify each expression.

uv 8 v

6 u − 3 v 8 v

m − 3 n 6 m^3 n

m + 3 n 6 m^3 n

a^2 + 3 a + 2

  • 5 a^ + 1 a^2 + 3 a + 2

10 n^2 + 16 n + 6

  • n^ − 6 10 n^2 + 16 n + 6
  1. r^ + 6 3 r − 6
  • r^ + 1 3 r − 6
  1. x^ + 2 2 x^2 + 13 x + 20 − x^ + 3 2 x^2 + 13 x + 20

x − 1 − 5 x 4

  1. 6 − x^ + 5

( 7 x − 5)( x + 4)

x + 7

x − 8

4 v^2 + 4 v

12 x − 8

n + 5

  • 4 n 2 n + 6
  1. 2 x 5 x + 4
  • 6 x 2 x + 3

3 x^2 + 12 x

2 x

  1. 7 n n + 1

n − 7

n + 8

n + 1

3 x + 4

b − 8

b + 3

x + 6

x − 2

x + 1

x + 2

5 n + 5 5 n^2 + 35 n − 40

7 n 3 n

n − 5

3 n − 8

a 25 − a 5 a

m

m

Critical thinking questions:

  1. Simplify: a b

c d

  1. Split into a sum of two rational expressions with unlike denominators: 2 x + 3 x^2 + 3 x + 2
  1. 7 n n + 1

n − 7 7 n^2 − 41 n + 8

( n + 1)( n − 7)

n + 8

n + 1 6 n + 34

( n + 1)( n + 8)

3 x + 4 9 x − 12

8 ( 3 x + 4)

b − 8

b + 3 10 b − 47

( b + 3)( b − 8)

x + 6

x − 2 10 x + 36

( x + 6)( x − 2)

x + 1

x + 2 2 x + 6

( x + 1)( x + 2)

5 n + 5 5 n^2 + 35 n − 40

7 n 3 n 52 n − 53 + 7 n^2

3 ( n + 8)( n − 1)

n − 5

3 n − 8 15 n − 54

( 3 n − 8)( n − 5)

a 25 − a 5 a

m

m 5 m 4

Critical thinking questions:

  1. Simplify: a b

c d ad + bc bd

  1. Split into a sum of two rational expressions with unlike denominators: 2 x + 3 x^2 + 3 x + 2

Many solutions. Ex: 1 x + 1

x + 2