Quiz 8-5

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Quiz 8-5
What is the simplified answer?
1.
2.
3.
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8-6 Solve Rational Equations
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Vocabulary
What does solve a single variable equation mean?
3x 2 11
What is a factor?
What is a least common multiple?
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Solving Rational Equations
Method 1 eliminate the denominators one at a
time.
Method 2 Obtain common denominators for each
term.
Method 3 Find the least common multiple of all
the denominators then
multiply (left/right) by the LCM.
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Rational Equations
How do you get the 5 out of the denominator?
x 20
Multiply both sides by 5
How do you get the x out of the denominator?
2x 10
Multiply both sides by x
x ?
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Your turn
1. Solve
2. Solve
3. Solve
4. Solve
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Variable on both sides of the equation
How do you get the x out of the left-side
denominator?
Multiply both sides by x
How do you get the (x1) out of the right-side
denominator?
Multiply both sides by (x1)
Your turn 5. solve
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Another example
The book teaches you to cross-multiply (yuck!)
There is no property called cross multiply.
There are the properties of equality.
Cross multiplication is the result of
multiplying both sides by the left denominator,
then multiplying the both sides by the right
denominator.
DONT THINK Cross multiply!! Forget it
completely!!
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Eliminate one Denomiator at a time.
(4x 5)
(4x 5)
(x 1)
(x 1)
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Or obtain a common denominator
(x 1)
(4x 5)
(4x 5)
(x 1)
Multiply both sides by the common denominator
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Your Turn
6. Solve
7. Solve
8. Solve
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What about this wrinkle?
multiply to eliminate the denominators one at a
time
x
x
Now what?
Its a quadratic, solve the quadratic!
put into standard form !!!
Your turn 9. solve
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Rational equations with 2 solutions.
Your turn 10. Eliminate the denominator.
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Your turn
11. Solve
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Check for Extraneous solutions.
Your Turn
12. Solve. 13. Check to see if either one
is extraneous.
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Multiply for the LCD
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Multiply both sides by the LCD!!
What is the least common denominator?
Factor the denominator
1. Look for what is common to each denominator.
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2. What does the 1st denominator need to be
common with the other two denominators?
Needs a 2
3. What does the 2nd denominator need to be
common with the other two denominators?
Needs an x
4. What does the 3rd denominator need to be
common with the other two denominators?
Needs an 2
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Find the least common denominator
2
3x 23 3x
2
x
The least common denominator is 6x
Multiply both sides by the LCD.
6x
6x
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Find the least common denominator
The LCD is 6x
Multiply both sides by the LCD.
6x
6x
Notice how I factored 6x so that it is easier to
simplify.
Wow ! x 4