Transcript Rational Equations

Rational Equations
Section 8-6
Objectives
• Solve rational equations with one variable
by CROSS MULTIPLYING
• Check answers for Extraneous Solutions
Extraneous Solutions
• Any solution that makes a denominator
ZERO does not check. (Extraneous)
Solving Rational Equations
• Two basic methods
• 1. Cross Multiply two rational expressions
to solve them
• 2. Set equation equal to ZERO and then get
Common Denominator
Today
• Cross Multiplying Method
Cross Multiplication Method
24
36

x3
x3
36( x  3)  24( x  3)
36x  108  24x  72
12 x  180
x  15
Example 2
x3 2

9
x
x( x  3)  9(2)
x  3 x  18
2
x  3x  18  0
2
( x  6)( x  3)  0
x6
x  3
Example 3
x2 x4

0
x
x6
( x  2)( x  6)  x( x  4)
x  8 x  12  x  4 x
2
2
 4x  12
x3
x2 x4

x
x6
EXAMPLE 1
Solve:
Solve a rational equation by cross multiplying
3 = 9
x + 1 4x + 1
3 = 9
x + 1 4x + 1
Write original equation.
3(4x + 5) = 9(x + 1)
Cross multiply.
12x + 15 = 9x + 9
3x + 15 = 9
3x = – 6
x=–2
Distributive property
Subtract 9x from each side.
Subtract 15 from each side.
Divide each side by 3.
ANSWER
The solution is –2. Check this in the original equation.
Homework
• WS 12-5