Lesson 33 Section 6.4Rational EquationsRemember that a fraction cannot have a zero denominator. Because a rational expressioncannot have a zero denominator, you must determine any values of x that would make a zero denominator. These value(s) are restricted from the domain. For example: 3033532xxxxx0)2)(2(044422xxxxx0)3(2062621322xxxxxxx20223444xxxx202xx 202xx002xx 303xxThis is impossible.Caution: Any number that makes a zero denominator in a rational expression or a rational equation cannot be in the domain. In other words, it cannot be x.To Solve a Rational Equation:1. Factor the denominators and find the LCD.2. Determine what values of x are restricted from the domain.3. Multiply each side of the equation (multiply each term of each side) by that LCD. This should ‘clear out’ the denominators.4. Solve appropriately.5. Disregard any possible solution(s) that are restricted from the domain.Examples:1)265xx2)nn 232213)57451023 yy)5(2 yLCD= )5(4 y505yy533528531282556)7(4)5(5)3(257)5(445)5(4)5(23)5(4yyyyyyyyyy534)xxxxxx5155432 )5( xxLCD = )5( xx5,0
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