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Section 9-6 Solving Rational Equations and Inequalities Ryann Noe
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Rational equation: Rational Inequalities: any equation that contains one or more rational expressions Ex: Inequalities that contain one or more rational expressions Ex:
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Solving Rational Equations Easier to solve once fractions are eliminated Eliminate by using Least Common Denominator FRACTIONS
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Multiply out 33-4=x x=29 Answer!
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Find LCD then SolveCheck your solution LCD= 28(z+2) multiply (9z+18) + 84 = 21z + 42 9z + 102 = 21z + 42 60 = 12z 5 = z
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CHECK True so: Z=5
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Solving Inequalities Excluded values: 1.State the excluded values 2.Change the sign to equals and solve 3.Use the values found by solving to make a number line and then test points values that make the denominator equal to zero
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example: 1.The only excluded value is 0 2.Solve: 2+5=4a 7=4a a=
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On your number line draw vertical lines at the excluded number and your solution to separate into regions -3-20123 Then test a value in each section and see which number comes out true
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Test a= –1 This is NOT true so a<0 is not a solution
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Test a=1 True so: 0<a<
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Test a=2 This is NOT true so a> is not a solution This means that the final answer is 0<a<
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Homework Page 510 # 11-37 odd
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