Challenge Problem!
Work in your groups to do this problem:
12
x2  x
2x2  4x  6
x2 1
A.5 Methods for
Solving Equations
Failures are finger posts on the road to achievement.
-C. S. Lewis
Domain
Recall: The domain is the set of all x values for which an
expression exists.
Ex. Find the domain of the following expression.
3x  2
3x 3  4 x 2  9x 12

Solve vs. Simplify!
This is what we did before:
3
𝑥−4
− 2
𝑥 − 1 𝑥 − 2𝑥 + 1
SIMPLIFY
This is what we’re doing now:
3
1
7
=
+ 2
𝑥 − 2 𝑥 − 1 𝑥 − 3𝑥 + 2
SOLVE
Solving Rational Equations
Recall how to solve the following equation…
x 1 1 5x5x
  
2 3 36 6

Steps for Solving Rational Equations
Step 1: Factor all denominators completely.
Step 2: Determine the least common multiple.
Step 3: Multiply both sides by the LCM (distribute!).
Step 4: Solve the new polynomial equation using learned
methods.
Step 5: Check for any extraneous solutions in the original
equation.
Solving Rational Equations
Solve the equation.
7
3
11
7



1 (x 1)(x  2) (x 1)(x  2)
x  2 xx 1

Solving Rational Equations
What if we have one a little more tricky?!
5
2
 2
3x 1 3x  5x  2

Solving Rational Equations
Do with your groups and turn in!
Pg 998 #42, 78, 80
Solve or Simplify??
a)
c)
3
𝑥−4
− 2
𝑥 − 1 𝑥 − 2𝑥 − 24
𝑥
𝑥+3
−3
−
=
𝑥2 − 1 𝑥2 − 𝑥 𝑥2 + 𝑥
b)
d)
4(𝑥 − 2) 3
−3
+ =
𝑥−3
𝑥 𝑥(𝑥 − 3)
1
1
ℎ 𝑥+ℎ
1
2 − 𝑥2
Homework #6:
p.998
#41, 45, 46, 77, 79,
80
A.5 Methods for
Solving Equations
Failures are finger posts on the road to achievement.
-C. S. Lewis
Solving Absolute Value Equations
What does “absolute value” mean?
x 7
What is the meaning of this equation?

2x  3  7
Steps for Solving Absolute Value Equations
Step 1: Isolate absolute value on one side of the equation.
x a
Step 2: Rewrite the equation, removing the absolute value,
and plus/minus of the other side of the equation.
x  a

Step 3: Solve each equation for x.
xa
x  a

Step 4: Check for any extraneous solutions in the original
equation.

Solving Absolute Value Equations
Solve the following equation for x.
3x  1  9  2x

Homework #6:
p.998
#41, 45 – 59 odd,
77, 79
A.5 Methods for
Solving Equations
Failures are finger posts on the road to achievement.
-C. S. Lewis