1
Section 5.5 
Rational Equations
Definition:
Equations that contain at least one rational expression are called
rational equations.
LCD stands for the
“Least common denominator”.
Solving rational equations
In this section, we will be solving rational equations.
You'll know that you're doing one of these
types of problems because the instructions that will tell you to “solve for
x
,” or just to “solve.”
To solve these types of equations, what you’re
supposed
to do is to get a common denominator
and one fraction on each side of the equal sign by doing the steps from section 5.3.
Then once
there’s only one fraction on either side of the equal sign, you multiply by the least common
denominator of either side and simplify.
Then you solve for
x
using the algebra we learned
earlier this semester.
Here’s an example:
Solve
1
1
4
6
=
+
+
x
x
.
(1)
Get a single fraction on both sides of “=”:
1
1
)
4
(
4
7
1
1
)
4
(
)
4
(
1
)
)(
4
(
6
=
+
+
→
=
+
+
+
+
⋅
x
x
x
x
x
x
x
x
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 Spring '08
 Staff
 Equations, Fractions, Fraction, Elementary arithmetic, LCD

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