Unit Review 1 Name:_______________________

Concept #1 – Multiplying and Simplifying Rational Expressions

Strategy – Factor the numerator and denominator of each fraction is possible, then cancel

common factors from the numerator and denominator.

1. 2

2

3 5

3 15

x x

x x x

+

+ − 2.

2 2

2 2

2 4 3

2 1 3

x x x x

x x x x

− + +

+ + + 3.

9 2 2

4 5

81

36

x x y

y x y

Concept #2 – Dividing and Simplifying Rational Expressions

Strategy – Flip the fraction that follows the division sign. Factor the numerator and

denominator of each fraction, then cancel common factors from the numerator and

denominator.

4. ( )2

2 14410 24

3 36

xx x

x

−+ −

− 5.

2

2

9 22 2

5 24 3

x x x

x x x

− − +

+ − − 6.

2

2

2

4 2

x x

x x

− +

Concept #3 – Adding Rational Expressions

Strategy – Find a common denominator and change both fractions to have this

denominator. Add the numerators of each fraction and simplify.

7. 2 1 1

8 8

x x

x

− ++ 8.

12 4

5x+ 9.

2

1

2 2

x

x x x+

+ − +

Concept #4 – Subtracting Rational Expressions

Strategy – Find a common denominator and change both fractions to have this

denominator. Subtract the numerators of each fraction and simplify.

10. 2 22 4 8 5 6 1

3 3

x x x x− + − −− 11.

2

4 3

4 2

x

x x−

− + 12.

5 2

1 3x x−

+ +

Concept #5 – Complex Fractions/ Complex Rational Expressions

Strategy – Follow addition, subtraction steps to get a single fraction in the numerator and

a single fraction in the denominator. Then follow multiplication and division steps.

13. 2

2

3 1

15 3

31

xx xx

xx

+−−

−−

+−

Concept #6 – Solving Equations by multiplying by the LCD – check for false solutions! *If you get a value for x that makes the denominator of the original problem = 0, then it is a false solution.

14. 2 3

3 3

x x

x x=

+ − 15.

4 4 2 2

1 1

x x

x x

− −=

− +

16. 3 1 12

2x x− = 17.

3 2 14

2 5

x x+ −− =

Mixed Review!

Perform the indicated operation and simplify completely.

18. 2

2

3 5

3 15

x x

x x x

+

+ − 19.

2 2

5 6 12

4 16 3 4

x

x x x x

+ − − −

20. )2(

52

)2(

4 2

+

−++

+

+

xx

xx

xx

x= 21.

x

x x x2 9

3

3−+

−=

( )

22.

2

1

3 23

2 4

x

xx

x x

−+

+

+

= 23. x

x x x x

+

−−

+−

+ −

2

1

2

6

14

5 62

24. 4 5

12x x

−+ =

− 25.

2

5 2

33 xx x=

−−