Solving Rational Equations

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

Solving Rational Equations

Rational Equation

Contains Rational expressions

6 = x

x+5 6

Solving Rational EquationsCross Products

6 = x 6(6)=x(x+5) 1. Cross multiply

x+5 6 36=x2+5x0=x2+5x-36 2. set quadratics

equal to zero

0=(x+9)(x-4) 3. factor

x+9=0 x-4=0 4. solve each for

x=-9 x=4 zero

Solving Rational EquationsCross 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 = x2-14x0= x2-14x+48

0=(x-6)(x-8)

X-6=0 x-8=0

X=6 x=8

Solving Rational EquationsMultiply 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.

Solving Rational EquationsMultiply by the LCD

3x - 5 = 5 LCD (x+5)(2) x+5 2 x+53x(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=10X-25=10X=35

Multiply everything by the entire LCD

Cancel out like terms between top and bottom

Expand-distribute

Combine like terms

Solve

Solving Rational EquationsMultiply 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

SolveLCD 5(x+10)

x(5)+x+10 = -7(5)

6x+10 = -35

6x = -45

x = - 15/2 or -7.5

Solving Rational EquationsFactor First

Sometimes you have to factor the bottom first.

4 + 1 = 14

x-4 x2+x-20

(x-4)(x+5)

Now work with a common denominator

Solving Rational Equations

Project Rational SearchMaterials:LaptopsInstructions: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.

Rational Search Sites

http://www2.nemcc.edu/RHawkins/alglessons/solve_rational_equations.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

Solving Rational Equations

Homework Page 178 (1-15)