Sec-55-beatrice-filled

# Sec-55-beatrice-filled - Definition An extraneous solution...

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Math 1300 Section 5.5 Notes Rational Equations Definition : Equations that contain at least one rational expression are called rational equations . Solving rational equations In this section, we will be solving rational equations. You'll know that you're doing one of these types of problems because the instructions that will tell you to “solve for x ,” or just to “solve.” The trick is to find the LCD of all the fractions in the problem (if a piece of your problem isn’t a fraction, make it into one by putting it over 1), and then multiply every piece of the problem by that LCD, simplify and solve.

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Math 1300 Section 5.5 Notes Example 1: 6 1 4 1 x x + + =
Math 1300 Section 5.5 Notes Extraneous Solutions There’s one last thing that you have to check before you’re done with the problem. Remember the definition of a restriction from back in section 5.1? Definition : A restriction on a rational expression is the value that would make the denominator equal to zero.

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Unformatted text preview: Definition : An extraneous solution is a value that is obtained from solving an equation that does not satisfy the original equation. You have to check that the solutions you get don’t include any numbers that are the restrictions on the rational expressions in the problem. Here’s an example of why you need to check: Math 1300 Section 5.5 Notes Example 2: 6 3 2 6 3 2 x x x =---Math 1300 Section 5.5 Notes Examples: 1. 2 5 3 3 6 4 x x + = Math 1300 Section 5.5 Notes 2. 3 4 6 8 1 x + = + Math 1300 Section 5.5 Notes 3. 5 13 1 7 2 14 4 2 x x-= + + Math 1300 Section 5.5 Notes 4. 2 3 6 24 4 4 16 x x x-=-+-Math 1300 Section 5.5 Notes 5. 2 3 5 8 x + = Math 1300 Section 5.5 Notes 6. 2 7 6 x x x x--= +-Math 1300 Section 5.5 Notes 7. 1 1 10 7 ( 2) ( 4) 1 x x---= Math 1300 Section 5.5 Notes 8. 2 1 7 49 2 14 7 x x x x-=-+-Math 1300 Section 5.5 Notes 9. 2 x-1 – x-2 = 1 Math 1300 Section 5.5 Notes 10. 6 9 4 2 1 x x-= - --...
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Sec-55-beatrice-filled - Definition An extraneous solution...

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