Study Guide and Intervention (continued) - MathnMind
Study Guide and Intervention (continued) - MathnMind
Study Guide and Intervention (continued) - MathnMind
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12-9<br />
NAME ______________________________________________ DATE ____________ PERIOD _____<br />
<strong>Study</strong> <strong>Guide</strong> <strong>and</strong> <strong>Intervention</strong> (<strong>continued</strong>)<br />
Solving Rational Equations<br />
Extraneous Solutions When you use cross multiplication or use the LCD of two<br />
rational expressions, you may get values for the variable that are not solutions of the<br />
original equation. Such values are called extraneous solutions.<br />
Example<br />
Solve .<br />
30(x 1) 5(x2 15 5<br />
<br />
x2 1 2(x 1)<br />
15<br />
<br />
x2 1<br />
1) Cross multiply.<br />
5<br />
Original equation<br />
2(x 1)<br />
30x 30 5x 2 5 Distributive Property<br />
0 5x 2 30x 30 5 Add 30x 30 to each side.<br />
0 5x 2 30x 25 Simplify.<br />
0 5(x 2 6x 5) Factor.<br />
0 5(x 1)(x 5) Factor.<br />
x 1 or x 5 Zero Product Property<br />
The number 1 is an extraneous solution, since 1 is an excluded value for x. So, 5 is the<br />
solution of the equation.<br />
Exercises<br />
Solve each equation. State any extraneous solutions.<br />
6x 2x 8<br />
4x 1<br />
1. 4 2. <br />
x 1 x 1<br />
x 2 x 2<br />
5 x 1<br />
x 4<br />
3. 4. x<br />
x 2 3<br />
x 3 3 x<br />
x 4<br />
x 1<br />
5. x 6. <br />
x 2 2 x<br />
x2 25 x 5<br />
x 1<br />
4z<br />
6 4<br />
7. 0 8. x2 36 x 6<br />
z2 4z 3 z 3 z 1<br />
p 2<br />
9. 4 10. x2 x<br />
16<br />
2 4<br />
16<br />
<br />
4 p p 4<br />
x 4<br />
© Glencoe/McGraw-Hill 754 Glencoe Algebra 1
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