Name__________________________________________ Date __________________________ Period______
Algebra 2
Chapter 8
Test Review
Guidelines to Simplifying Rational Expressions:

Factor the numerator, if possible

Factor the denominator, if possible

Look for common factors, if any

Cancel common factors
Simplify.
1.
x 2  3x  28
x7
2.
x4
x 2  16
3.
3x 2  15 x
x5
4.
x 2  13x  42
x 2  3x  2
Guidelines to Multiplying Rational Expressions:

Factor the numerator and denominator of each fraction.

Cancel common factors:
o Up and Down and Diagonally

Multiply numerator by numerator and denominator by denominator
Guidelines to Dividing Rational Expressions:

Rewrite the problem into a multiplication problem.
o First Fraction stays the same
o Division sign changes to a multiplication sign
o Take the reciprocal of the second fraction

Factor the numerator and denominator of each fraction.

Cancel common factors:
o Up and Down and Diagonally

Multiply numerator by numerator and denominator by denominator
Multiply or Divide. Express each product in simplest form. Assume no denominator equals zero!
5.
3x  6 x  2

16 x
4x 2
6.
9
 8  12 x 
2  3x
7.
x 2  6x  8
 3x  12
x2
8.
x  9 x 2  2x

x9
x2  4
Guidelines to find Least Common Denominator:

Factor the denominator, if possible

Look for lowest number that each denominator goes into

For variables, choose the higher exponent.

Choose common quantity once
Find the LCD of each group of fractions.
9.
3u
u
a 1
b
_______________
,
, 2 _______________ 10.
4
5v 5v  25
12 xy 3 x y
Guidelines to Adding and Subtracting Expressions:
1. Check to see if the fractions have the same denominator.
2. If not, find the least common multiple of the denominators
3. Rewrite the problem using the LCD.
4. Add/subtract the numerators and keep the same denominator.
5. Simplify your answer by looking for common factors.
Recall: You may have to factor to simplify.
Add or Subtract. Assume no denominator equals zero!
12.
5x
2x  1

x3 x3
13.
a3
5

2
6a  12a 12a 2
14.
x 1 x  5

2x
3x 2
15.
2
9

x  1 4x  4
11.
y y  10
_______________
,
z z  15
Guidelines to solve fractional equations:
1. Factor the denominator, if needed.
2. We must state restrictions for denominators when solving rational equations and check our solution!
3. Find the LCM of the denominators.
4. Multiply each term by the LCM (this will cancel the denominators!).
5. Solve the remaining equation.
6. Check your solution with restriction(s)!
State restriction(s) and solve each equation.
16.
y
3
18

 2
y 3 y 3 y 9
17.
3
1 1
 
x 1 x 2
18.
1
3

0
z  3 3z  9
19.
k 3k k

 1
3 10 5
20.
2
1
8

 2
x  5 x  2 x  3 x  10
21.
5y 1 1

1 5y 4