Learning Lab Supplement by C. Pierce
Jackson County Campus
RATIONAL EQUATIONS
To solve an equation containing fractions, clear denominators by multiplying each term
of the equation by the least common multiple, LCM, of the denominators. Then solve for
the variable. Occasionally, a value of the variable that appears to be a solution will make
one or more of the denominators zero. If that happens, the equation has no solution for
that value of the variable.
3X
5
SOLVE:
= 5−
The LCM is X - 5
Multiply each term by x - 5
X −5
X −5
 3X 
 5 
( X − 5)
 = ( X − 5)5 − ( X − 5)

 X −5
 X −5
3 X = 5 X − 25 − 5
3 X = 5 X − 30
SIMPLIFY:
− 2 X = −30
X = 15
15 checks as a solution.
SOLVE THE FOLLOWING RATIONAL EQUATIONS:
1.
3X
9
= 2+
X −3
X −3
2.
X 5 X
+ =
2 6 3
3.
X 2 X
− =
5 9 15
4.
4
2
=
X −4 X −2
5.
X −2
1
=
5
X +2
6.
X +4
6
=
10
X −3
7.
3X =
8.
X
10
=
X −1 X + 3
9.
4Y − 9
10.
5−
12.
1
1
2
− =
X − 2 6 3X − 6
14.
8
4
=
X − 2 X +1
4 13
−
X 2
2
2
+
1
3
=
2Y − 3 2Y + 3
11.
5
2
3
−
= 2
X −2 X +2 X −4
13
X +2=
24
X
2
3
=
2X − 5 2X − 5
15.
5
2
5
=
+
X − 7 X + 12 X − 3 X − 4
16.
6
2X
=
X + 5 X +1
17.
5 X − 22
11
5
− 2
=
2
X − 6 X + 9 X − 3X X
18.
1
5
4X + 2
−
= 2
X X −1 X − X
19.
X 20
+
=7
2 X
20.
4
7
= 2+
2
X
X
2
ANSWERS:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
NO SOLUTION
X=-5
X = 5/3
X=0
X = -3, X = 3
X = -9, X = 8
X = -8/3,X = ½
X = 2, X = 5
X = 7/2
X=3
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
X = -11/3
X=4
X = -6, X = 4
X=-4
NO SOLUTION
X = - 3, X = 1
X=-4
X = - 3/8
X = 4, X = 10
X = ½, X = - 4