Algebra 2 Chapter 8 Review
Rational Functions
RATIONAL EXPRESSIONS
AND EQUATIONS
MATCH TO THE CORRECT PROCESS FOR APPROACHING
THE PROBLEM
x2
2(x  3)
2
Solve:
3x  1
3x  1
A. Factor, find the LCD, and rewrite each fraction with the
LCD. Simplify by combining like terms in the numerator. The
resulting denominator is the LCD.
3x
2
Simplify: 2x  1
5
x

4x 2x  1
B. Divide the coefficients of the highest power in the
numerator and denominator
1.
2.
3. Simplify:
x 2  4x
x 2  2x  24
4.
Perform the indicated
operation
3x
2
 2
x  5 x  25
5.
Perform the indicated
operation
3
x  9x x 3  3x 2

x 2  6x  9 x  3
C. Take the cube root of each term and substitute the values
into the formula for the sum of two cubes
D. Multiply the small fractions by their LCD in order to
eliminate their denominators, then simplify
E. Multiply the first expression by the reciprocal of the
second expression. Factor completely and cancel like factors
between the numerator and denominator
6. Factor: x 3  64
D. Multiply the small fractions by their LCD in order to
eliminate their denominators. Solve the remaining equation.
7. Perform the indicated
operation
2
x

3x 1 3x 1
E. Factor completely and cancel like factors between the
numerator and denominator
8. Perform the indicated
operation
2
3x  4x  1
x 1
 2
2
x 4
x  8x  12
F. Add the numerators since the denominators are the same.
The new expression will have the same denominator
9. Find the horizontal
asymptote
x 2  10x  11
x 2  7x  8
G. Factor completely and cancel like factors between the
numerators and denominators. Factors can be cancelled
across both expressions.
Algebra 2 Chapter 8 Review
Rational Functions
Perform the indicated operation(s). Simplify the
result.
Perform the indicated operation(s) and simplify.
5.) Add:
1.) Simplify:
2.) Multiply:
3.) Divide:
4𝑥−4𝑥 2
8𝑥 3 −27
25𝑥 2 𝑦 3
35𝑧 5
•
÷
4𝑥 2 +6𝑥+9
4𝑥
6.) Subtract:
2𝑦 9 𝑧 3
7.) Add:
𝑥 5𝑧 8
7𝑥+1
𝑥 2 −5𝑥−6
+
8
𝑥−6
−
3
𝑥+1
4.) Divide:
Simplify the complex fractions.
8.)
9.)
Answer the following questions based on what you know about graphing rational functions.
10.) How do you write vertical asymptotes?
11.) How do you write horizontal asymptotes?
12.) Where in the equation do you look to find the vertical asymptote?
13.) How is the process for identifying holes different from identifying vertical asymptotes?
14.) How do you find the horizontal asymptote from the equation of a simple rational function?
15.) How do you find the horizontal asymptote from the equation of a general rational function?
𝑥 2 −25
16.) What is the vertical asymptote(s) of y =
?
𝑥−3
17.) What is the horizontal asymptote of y =
18.) Does y =
?
have a horizontal asymptote? How do you know?
Algebra 2 Chapter 8 Review
Rational Functions
19.) What is the horizontal asymptote of y =
20.) What is the horizontal asymptote of y =
? Vertical asymptote(s)?
𝑥+4
? Hole?
𝑥2 −16
21.) Pre-AP: For problems 16-20, find the slant asymptote, if it exists.
Graph each function and identify important characteristics.
22.) y =
a. Vertical asymptote
b. Horizontal asymptote
c. Transformations
d. Domain and Range
23.) y =
a.
b.
c.
d.
Vertical asymptote(s)
Horizontal asymptote(s)
Hole(s)
Domain and Range
24.) y =
a.
b.
c.
d.
Vertical asymptote(s)
Horizontal asymptote(s)
Hole(s)
Domain and Range
25.) y =
a.
b.
c.
d.
𝑥 2 −4𝑥−5
𝑥 2 −25
Vertical asymptote(s)
Horizontal asymptote(s)
Hole(s)
Domain and Range
Identify any excluded values, then solve each equation. Check for extraneous solutions.
31.)
34.)
32.)
35.)
33.)
36.)