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# Sec-55 - Math 1300 Rational Equations Section 5.5 Notes...

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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.” To solve these types of equations, what you’re supposed to do is to get a common denominator and one fraction on each side of the equal sign by doing the steps from section 5.3. Then once there’s only one fraction on either side of the equal sign, you multiply by the least common denominator of either side and simplify. Then you solve for x using the algebra we learned earlier this semester. Here’s an example: 1 1 4 6 = + + x x (1) Get a single fraction on either side of “=”: 1 1 ) 4 ( 4 7 1 1 ) 4 ( ) 4 ( 1 ) )( 4 ( 6 = + + = + + + x x x x x x x x x (2) Multiply by LCD of both denominators and simplify: 1 1 1 ) 4 ( ) 4 ( 4 7 1 ) 4 ( = + + x x x x x x x (3)

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