Brought to you by: Jordan Green and Chelsea Caldwell 8.6 Solving Rational Equations 8.6 Objectives

* I will learn to solve rational equations

* I will learn how to use ration equations to solve problems Vocabulary Rational equation- an equation that contains at least one rational expression. Solving Let's solve the following equation Example: x + x = 2 x+1 x-1 x 2 -1 Not A Rational Expression:

1 = 2 2 3 x+ x + x = 8 x+6 x-6 x -36 2 Factor the denominators to find the LCD. How many

licks does it

take to get to

get to the

center of a Tootsie

Pop? x + x = 8 x+6 x-6 (x-6)(x+6) Multiply both sides by the LCD to remove the denominator x + x (x+6) = 8 x+6 x-6 (x+6)(x-6) (x-6) (x+6) (x-6) Now simplify and solve. x- 6x + x + 6x= 8 2 2 2x = 8 2 2 2 x = 4 2 x = 2 Check for extraneous solutions. http://blueshirtkhakipants.wordpress.com/category/rational-expressions-a-comic-strip/ You Try x/(x+6)+x/(x-6)=8/(x^2-36) 2/(2+6)+2/(2-6)=8/█(2^2-36) 2/8+2/(-4)=8/(-32) (-2)/(-2+6)+(-2)/(-2-6)=8/(-2^2-36) (-2)/4+2/8=8/(-32) NO EXTRANEOUS SOLUTIOLNS 1. j/(j+5)+j/(j-5)=j5/(j-25) 2. b/(4-b)-b/(4+b)=8/(16-b^2) 3.(a-1)/(a^2-9)+2a/(a^2)=(3a+2)/(a-3)

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# 8.6 Lesson: Solving Rational Equations

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