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 xy y xy 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 2 144 10 24 3 36 x x 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 5 x + 9. 2 1 2 2 x x x x + + − +
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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.
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.