Name__________________________________________ Date __________________________ Period______
Algebra 2A Chapter 11
Chapter 11 Test Review
Guidelines to Solve Equations using Cross Products:

Cross Multiply (diagonally)

Solve remaining equation.
Solve using cross products.
x6 x4

7
3
1.
3.
3 x

8 12
2.
x 1
x

x
x3
4.
4
3

x 1 x  2
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.
x 2  3x  28
5.
x7
6.
x4
x 2  16
Simplify.
7.
3x 2  15 x
x5
8.
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!
9.
3x  6 x  2

16 x
4x 2
10.
9
 8  12 x 
2  3x
Multiply or Divide. Express each product in simplest form. Assume no denominator equals zero!
x 2  6x  8
 3x  12
x2
11.
12.
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.
13.
a b
,
_______________
2 x 3x
14.
3u
u
,
_______________
7 w 7 w  21
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.
15.
8 x 10
,
_______________
x2 x
Add or Subtract. Assume no denominator equals zero!
16.
5x
2x  1

x3 x3
17.
a3
5

2
6a  12a 12a 2
18.
x 1 x  5

2x
3x 2
19.
2
9

x  1 4x  4
We must state restrictions for denominators when solving rational equations and
check our solution!
State restriction(s) and solve each equation.
20.
y
3
18

 2
y 3 y 3 y 9
21.
3
1 1
 
x 1 x 2