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Math 35
6.7 "Solving Rational Equations"
Objective:
* Solve rational equations.
Solve Rational Equations
Solving Rational Equations
1. Factor all denominators.
2: Determine which numbers cannot be solutions of the equation.
3: Multiply both sides of the equation by the LCD.
4: Use the distributive property to remove parentheses.
5: Remove any factors equal to 1, and write the result in simpli…ed form.
6: Solve the resulting equation.
7: Check all possible solutions in the original equation.
Example 1: (Solving rational expressions)
Solve the following equations.
3
7
a)
+
=2
5 x+2
c)
2
x
3
=
x
x2
9
+
4
x+3
b)
1
1
=
b
8
d)
2
2y
1
1
+
=
y + 4 y 2 + 2y 8
y 2
Page: 1
3
8b
Notes by Bibiana Lopez
Intermediate Algebra by Tussy and Gustafson
6.7
Example 2: (Solving rational expressions with opposite factors)
1
1
1
Solve the following equation.
+
=
6y 6 1 y
6
Solve Rational Equations with Extraneous Solutions
When we multiply both sides of an equation by a quantity that contains a variable, we can get false solutions, called
extraneous solutions. This happens when we multiply both sides of an equation by 0 and get a solution that gives a 0 in
the denominator of a rational expression. Extraneous solutions must be discarded.
Example 3: (Solving equations with extraneous solutions)
Solve the following equations.
t 3
1 2t
=
a) 3
t+2
t+2
b)
Page: 2
3
x
4
+
2
18
+
x + 5 x2 + x
20
=0
Notes by Bibiana Lopez