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 Equations
Cross Products
6 =
x+5
x
6
6(6)=x(x+5)
36=x2+5x
0=x2+5x-36
0=(x+9)(x-4)
x+9=0
x-4=0
x=-9
x=4
1. Cross multiply
2. set quadratics
equal to zero
3. factor
4. solve each for
zero
Solving Rational Equations
Cross Products
You try:
-12 = x-14
x
4
-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
1. Cross multiply
2. Distribute
3. Factor
4. Set to zero if quadratic
5. Solve each set of parentheses.
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.
Solving Rational Equations
Multiply by the LCD
3x - 5 = 5
LCD (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
Solving Rational Equations
Multiply by the LCD
Try onex
+ 1 = -7
X+10 5 x+10
Multiply everything by the entire
LCD
Cancel out like terms between
top and bottom
Expand-distribute
LCD 5(x+10)
Combine like terms
Solve
x(5)+x+10 = -7(5)
6x+10 = -35
6x = -45
x = - 15/2 or -7.5
Solving Rational Equations
Factor 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 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.
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-PowerPoint
Solving Rational Equations
Homework Page 178 (1-15)