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Solving Equations Containing Rational Expressions
The general method used involves multiplying both sides of the equation by the lowest common denominator,
stating any necessary restrictions. This will eliminate the rational expressions from the equation.
examples:
x
4
±
3
x
±
5
2
=
1
3
!
lcd
= 12
12
²
x
4
±
3
x
±
5
2
±
= 12
²
1
3
±
3 (
x
)
±
6 (3
x
±
5)
= 4 (1)
x
=
26
15
2
x
±
2
±
3
x
+ 1
= 0
!
lcd
= (
x
±
2) (
x
+ 1)
(
x
±
2) (
x
+ 1)
²
2
x
±
2
±
3
x
+ 1
±
= (
x
±
2) (
x
+ 1)
²
0
,
x
6
=
±
1
;
2
(
x
+ 1) (2)
±
(
x
±
2) (3)
= 0
x
= 8
x
±
1
x
+ 2
=
x
±
3
x
+ 1
+
2
x
(
x
+ 2) (
x
+ 1)
(
x
+ 1) (
x
±
1)
= (
x
+ 2) (
x
±
3) + (1) (2
x
)
,
x
6
=
±
2
;
±
1
x
2
±
1
=
x
2
±
x
±
6 + 2
x
5
=
x
1
x
+
1
x
±
3
=
x
±
2
x
±
3
(
x
±
3) (1) + (
x
) (1)
= (
x
) (
x
±
2)
,
x
6
= 0
;
3
x
2
±
4
x
+ 3
= 0
(
x
±
3) (
x

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