Alg 3(11) Ch 4.3 & 3.4
Radical / Rational Equations
Algebra 3 Assignment Sheet
(1) Assignment 1

Radical Equations
(2) Assignment 2

Rational Equations
(3) Assignment 3

Assorted Equations
(4) Review Worksheet
(5) TEST
1

4)
Alg 3(11) Ch 4.3 & 3.4
Radical / Rational Equations
RADICAL EQUATIONS
2
Don’t forget that radicals have restrictions!! _________________________________
I Principle for solving radical equations
The opposite of taking a root is taking it to a power.
METHOD:

Isolate the radical

Square each side.

Check your answers
II EXAMPLES
1) x

2

2

5
2) x

4 + 2 = x
3) x
2 
9
 
5 x

16
 x

4

Alg 3(11) Ch 4.3 & 3.4
Radical / Rational Equations
(1) 2

1

3
(2) x

3

2 x
(3) 6

1

2

1
(7)
(4) x

4

2
  x
(5) 5

1

5

3x
(6) 3 x
2 
2
 x

2
2 x
3 
2
 x

1
Algebra 3 Assignment #1
Solve for x please .
3

Alg 3(11) Ch 4.3 & 3.4
Radical / Rational Equations
(1) 4
(2) 1
 reject
 3
4

(3) 0 ,
1
2
(4) -3 ( reject 0 )
(5) 3
 reject
8
9

(6)

1 , 3
(7)

1 , 1 ,
1
2
Alg 3 Assignment #1 Answers
4

Alg 3(11) Ch 4.3 & 3.4
Radical / Rational Equations
3.4 RATIONAL EQUATIONS
Method

Factor denominators

Find the LCD

Multiply every term by the LCD

Reduce away the denominators, multiply the numerator by the remaining factor(s).

Solve the equation

Check your answer Restrictions?
Examples
1) x
 x
3

2
3

10
2)
3x

2
4

3

1
2
3)
4  
5

4
3
 x

2
 
2
5

Alg 3(11) Ch 4.3 & 3.4
Radical / Rational Equations
4)
5 x
2 
9

3 x

3

 x

2
5)
3
2x
2 
3x

2
6)
 x

2

2

2x x 2  
2
= 0
6

Alg 3(11) Ch 4.3 & 3.4
Radical / Rational Equations
Algebra 3 Worksheet #2
Solve each of the following for x please.
(1)
5 x
3

1

3 x
5

1
(2) x

2
3 x + 2

3 x

1 x + 8
(3)
3 x

5

2
4x + 5
12
 x

3
6

1
(4)
3 
4
 
1
3
  5
6

5x

14

(5)
5 x x


3
+
2
2x

1
 x

3 x
16x
2
+ 33
+ x

6
= 1

2x x + 3
(6)
4 x

1

4
2x

3
3

3x + 8

2

12
2 x

1
2
(7)
3
2

2
3 x
 3
4
 
6
1
2 x +
3
5

=
1
3

2x
 3
4


2
(8)
2x + x

3
1

3x
 x + 1
1
 x
2
8x

1
= 2
7

Alg 3(11) Ch 4.3 & 3.4
Radical / Rational Equations
Rational Equation Worksheet Answers
1
(1)
2
(2) 2 ,

9
8
17
(3)
12
(4) 4
(5)
–1
41
(6)
29
(7)
15
2
4
(8)
3
8

Alg 3(11) Ch 4.3 & 3.4
Radical / Rational Equations
Algebra 3 Assignment # 3
Solve for x please.
(1) 8 x

1

2x

x

4
(2) 9 x

2

3x

2
(3) 5 x

4
 x

1

1
(4)
3 3   3 2
x
 
(5)
5 x
2x


3
1

5x
3x

4

1
(6) x
2
2 x


1
x

2
 x
2 x

1

4x

3
 x x

2
2 
x

6
(7) x
2
2 x

1

3x
 x
3x
2

2

3x
 x
10
2 
9
(8)
5x

2 x

1

2x

3 x

1
 x

9 x

1

2x
9

Alg 3(11) Ch 4.3 & 3.4
Radical / Rational Equations
(1) 3
 reject
5
9

(2) 2
 reject
1
3

(3) 0
 reject
 3
4

(4) 2,

2 ,

1
(5)

1

10
21
(6)
 3
2
 reject 1

(7)
 3
5
 reject 3

(8)

2
 reject 1

Mixed Review Answers
10

Alg 3(11) Ch 4.3 & 3.4
Radical / Rational Equations
Algebra 3 Review Worksheet
Solve for x.
(1) 2x

1

x

1 (2) 8 x

1

5

2x
11
(3) 2x
2 
1

x

2 (4) 2 x

3

1

5x
(5) x
  
x

3 (6) 4 x

1
 x

1

2
(7) x x


3
2

3x x


1
1
(8) x

1

3 x
2 
1

1

12
2x

5
4
(9) x
2
2x


1
x

6
 x
2
3x

1

5x

6
 x
20x
2 
9
(10) x
2
4x

3

3x

2
 x
2
9x

5

4x

3
 x
2x

5
2 
5x

6
(11) x
3x
2

1

x
 x
2x
2

1

x

2 x

6 x
3 
x
(12) x
2 x

1

3x

2
 x
2
9x

4
 x x
2 
5
2 
x

2

Alg 3(11) Ch 4.3 & 3.4
Radical / Rational Equations
(1) 4 (reject 0)
(3) 5 ,

1
(5)

3 ,

6
(7)

1
2
, 5
2
(9)
15
(reject -3)
6
(11)
7
(reject -1)
Answers
(2) 6 (reject 1)
(4)

11
25
(reject 1)
(6)
10
9
(8) 5

31
4
(10)
7
, 2
(reject 1)
(12) 1 , 8 (reject -1)
12