Page 677 - Algebra 1

L E S S O N Solving Rational Equations 99
Warm Up
New Concepts
1. Vocabulary The denominator of a contains a variable. The
(39)
Find the LCM. 2. 7x2y and 3xy3
(57)
4. (x + 3) and (2x - 1) (57)
value of the variable cannot make the denominator equal to zero.
3. (3x - 6) and (9x2 - 18x) (57)
5. (14x - 7y) and (10x - 5y) (57)
A rational equation is an equation containing at least one rational expression. There are two ways to solve a rational equation: using cross products or using the least common denominator.
Either way may lead to an extraneous solution; that is, a solution that does not satisfy the original equation. The solution may satisfy a transformed equation, but make a denominator in the original equation equal 0. If an answer is extraneous, eliminate it from the solution set.
If a rational equation is a proportion, it can be solved using cross products.
Solving a Rational Proportion
Solve each equation. a. _3=_5
Math Language
A rational expression is a fraction with a variable in the denominator.
Example
1
x x-6 SOLUTION
_3 = _5
x x-6
3(x - 6) = 5x 3x - 18 = 5x -18 = 2x
Use cross products. Distribute 3 over (x - 6). Subtract 3x from both sides. Divide both sides by 2.
Math Reasoning
Analyze Why is it necessary to keep the terms in the denominator grouped?
-9 = x
Check Verifythatthesolutionisnotextraneous.
Online Connection www.SaxonMathResources.com
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_3 = _5
x x-6
_3 _5
Substitute-9forxintheoriginalequation.
Simplify the denominator.
Simplify each fraction.
The solution is x = -9. ✓
-9 _3
-9 - 6 _5
-9
-_1 = -_1
662 Saxon Algebra 1