# Steps to solving a rational equation

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```GUIDED NOTES – Lesson 5-3
Solving Rational Equations
Name: ______________________ Period: ___
OBJECTIVE: I can solve rational equations, using the LCD
We are now ready to solve rational equations, applying much of the factoring and
simplification skills we have mastered in 5-1 and 5-2.
Remember that an equation is an equation because it has an _______________, without that
it is just an expression. Previously we were just simplifying for the sake of simplifying, now our
goal is to simplify and _________ for the variable.
Steps to solving a rational equation:
1. Factor all denominators
2. Find the LCD (least common denominator)
3. Multiply every term by the LCD (it will get rid of the denominator)
4. Solve for the variable in the numerator
x 1 2

15
5
2x  1
2
1


x 2  2x  8 x  4 x  2
2
1 2
 
x  4 x 3x
At this point, we need to watch out for a potential problem. Recall from previous math
0
courses the following: 
5
5

0
Division by zero is not possible, so any solution we find that would make the denominator = 0,
will not be a solution, we will call it an ___________________ solution.
For example, identify whether each of this solutions is S, a solution; N, not a
4
2
solution; or E, extraneous:

x  3 2x
x=3
3
1
2

 2
x  1 x 1 x 1
x=1
x=0
x = -1
x = -3
2
1
 x 2  3x

 2
x  3 x  1 x  2x  3
APPLICATION: Steve and Jake both work on a paint crew. Steve is new at the job and can
paint a house in about 12 hours. Jake is experienced and can paint a house in 9 hours. If their
boss sends them to paint a house together, how long will it take the
ℎ  ℎ
+
=1

```