Warmup Alg 2 27 Mar 2012

Agenda• Don't forget about resources on

mrwaddell.net

• Section 8.6: Solving Rational Equations• Multiplication• Adding & Subtracting• Cross multiplying• So we can solve

Section 8.6: Solving Rational EQUATIONS

Solving Equations by GRAPHING

Step 1: put each side in calculator on it’s own line.

Step 2: See where they cross.

Make sure you use parenthesis

Step 3: Eliminate Asymptotes if needed.

𝑥𝑥−6

=1

𝑥−4

𝑥𝑥−6

𝑥𝑥−6

1𝑥−4

x/(x-6)

1/(x-4)

Zoom in

x = 2, x = 3

Solving Equations - AlgebraStep 1: Find the asymptotes!

Step 3: Distribute

Step 2: Cross Multiply)6(1)4( xxx

642 xxx66 xx

0652 xx

x=6, x=4. Our answer CANNOT be one of these.

0)3)(2( xxSince x=2, and x=3 are not Asymp. We have 2 answers.

Step 4: Solve

𝑥𝑥−6

=1

𝑥−4

Solving Equations - AlgebraStep 1: Find the asymptotes!

Step 2: Distribute & Add

9

18

9

)3(2

9

)3(222

xx

xx

x

xx x=+3, x=-3. Our answer CANNOT be one of these.

Step 3: make it equal zero

9

18

9

62

9

322

2

2

2

xx

xx

x

xx

9

18

9

3322

2

xx

xx

𝑥𝑥−3

+2𝑥𝑥+3

=18

𝑥2−9

Solving Equations - Algebrax=+3, x=-3. Our answer CANNOT be one of these.

09

18

9

3322

2

xx

xx

09

18332

2

x

xx Step 4: factor or use quadratic formula.

09

)6(32

2

x

xx

09

)2)(3(32

x

xx

Since x=3 cannot be an answer, x = -2 is the only answer!

Some Cautions

1. Not every equation has an answer. Some equations have “No Solution”.

2. You will need to use the quadratic formula on some of the problems. They are not always factorable.

3. Whenever there is a question, GRAPH IT! The picture never lies.

Assignment

Section 8.6, page 593:

7 – 11,

15 – 22