342 Rational Functions 4.3 Rational Inequalities and Applications In this section, we solve equations and inequalities involving rational functions and explore associ- ated application problems. Our rst example showcases the critical dierence in procedure between solving a rational equation and a rational inequality. Example 4.3.1. 3 3 1. Solve x −2x+1 = 1x−1. 2. Solve x −2x+1 ≥ 1x−1. x−1 2 x−1 2 3. Use your calculator to graphically check your answers to 1 and 2. Solution. 1. To solve the equation, we clear denominators 3 x −2x+1 = 1x&minus ...
December 1, 2017 3.7 - Solving Polynomial and Rational Inequalities For more complicated inequalities, it is often useful to use a sign diagram. Steps for solving polynomial and rational inequalities: 1. Identify any real undefined values. 2. Rewrite inequality so one side is 0. 3. Find the real zeroes of the inequality from step 2. 4. Create a sign diagram using the zeroes and undefined values. Be sure to label points with open or closed circles Remember only zeroes can be closed circles, and only if the inequality is allowed to be equal to zero. Holes and Vertical Asymptotes ...
Ch 3.5 – Polynomial and Rational Inequalities DAY 6 HW: Page 193 #7, 9, 11, 15, 17, 19, 25, 29, 31, 33, 35, 37, 45, 57, 59 Pre-Calculus Warm-Up (before 3.5) Solve for x: 1. 2. Add or subtract the following fractions: (HINT: you need a common denominator!) 3. 4. Graph the following: 5. y =(x !3)2(x +2) 6. y = 2x !4 x +3 (HINT: remember end behavior & multiplicity of zeros!) y y x x Intervals above the x-axis: ___________________ Intervals above the x-axis: ___________________ Intervals below the x-axis: ___________________ Intervals below the ...
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