1. Solving Rational Equations MM1A3d Solve simple rational equations that result in linear equations or quadratic equations with a leading coefficient of 1.

2. Solving Rational Equations Rational Equation Contains Rational expressions 6=x x+56

3. Solving Rational Equations Cross Products 6=x6(6)=x(x+5) 1. Cross multiply x+5636=x 2 +5x 0=x 2 +5x-36 2. set quadratics equal to zero 0=(x+9)(x-4) 3. factor x+9=0x-4=0 4. solve each for x=-9x=4 zero

4. Solving Rational Equations Cross Products You try: -12 = x-14 x 4 1.Cross multiply 2.Distribute 3.Factor 4.Set to zero if quadratic 5.Solve each set of parentheses. -12(4) = x(x-14) -48 = x 2 -14x0= x 2 -14x+48 0=(x-6)(x-8) X-6=0x-8=0 X=6x=8

5. Solving Rational Equations Multiply by the LCD If there is more than one expression on a side of the equation, you cannot cross multiply. 3x - 5 = 5 x+5 2 x+5 See how there are two expressions on the left side.

6. Solving Rational Equations Multiply by the LCD 3x - 5 = 5LCD (x+5)(2) x+5 2 x+5 3x(x+5)(2) -5(x+5)(2) = 5(x+5)(2) (x+5) (2) (x+5) 3x(2)-5(x+5)=5(2) 6x-5x-25=10 X-25=10 X=35 Multiply everything by the entire LCD Cancel out like terms between top and bottom Expand-distribute Combine like terms Solve

7. Solving Rational Equations Multiply by the LCD Try one- x + 1 = -7 X+10 5 x+10 Multiply everything by the entire LCD Cancel out like terms between top and bottom Expand-distribute Combine like terms Solve LCD 5(x+10) x(5)+x+10 = -7(5) 6x+10 = -35 6x = -45 x = - 15/2 or -7.5

8. Solving Rational Equations Factor First Sometimes you have to factor the bottom first. 4 + 1 = 14 x-4 x 2 +x-20 (x-4)(x+5) Now work with a common denominator

9. Solving Rational Equations Project Rational Search Materials: Laptops Instructions: Go to at least three of the websites listed. Take notes on the presentations. Make sure your notes include at least three examples of problems worked out. Write a review of the websites by ranking them from 1 to 3 with 3 being the most helpful. Tell why you ranked them as you did. Find two more web based resources on the lesson and include them on your sheet to turn in.

10. Rational Search Sites http://www2.nemcc.edu/RHawkins/alglessons/solve_rational_equati ons.ppt http://teachers.henrico.k12.va.us/math/hcpsalgebra2/9-5.htm http://math.lhs.lusd.org/Algebra%201%20PowerPoint%20Lessons/ Chapter%2010/lesson%2010.6_Solving_Rational_Equations.ppt http://www.klvx.org/DocumentView.asp?DID=182 http://www.mathslideshow.com/Alg1PH/Lesson10-6/index.htm http://www.scribd.com/doc/9012673/Rational-Expression-Power- Point

11. Solving Rational Equations Homework Page 178 (1-15)