Rational Equations

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Rational Equations

• GPS Algebra
• Standard MM1A3d. Solve simple rational equations
  that result in linear equations or quadratic
  equations with leading coefficient of 1.

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Standard

• MM1A3. Students will solve simple equations.
• a. Solve quadratic equations in the form
• ax2 bx c 0, where a 1, by using
• factorization and finding square roots
  where
• applicable.
• c. Use a variety of techniques, including
  technology, tables, and graphs to solve equations
  resulting from the investigation of x2 bx c
  0.

Today
d. Solve simple rational equations that result in
linear equations or quadratic equations with
leading coefficient of 1.
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Essential Question

• What is the difference between a rational
  expression and a rational equation?
• What is an extraneous solution?
• How do you check for extraneous solutions?

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• This is a rational expression..

That looks familiar.
This is a rational equation
Whats the difference?
Rational equations have solutions!
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What does it mean to be a solution??
This means you can solve for x This means that
the function crosses the x-axis They are the
points were y 0
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Extraneous solutions(aka restriction on the
domain)

•  

You can never have ZERO in the denominator
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Extraneous solutions

• Extraneous solution is a solution that does not
  actually work.
• It is found mathematically but it is not allowed
• What can my denominator never be?
• Zero
• If I find a solution mathematically that makes
  the denominator zero than it is an extraneous
  solution

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Notes-Rational Equations

• Cross-multiply.
• Remember to distribute
• 3. If theres an x2 , bring everything to one
  side and factor. (Quadratic)
• If theres just an x, then solve by getting x by
  itself. (Linear)

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X
-4
-6 2
Cross Multiply
-12
Distribute
Solve the Quadratic
Write in factor form
x -2, 6
Check your answer
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Example Solve.
X
1
4 -3
Extraneous solutions You can NEVER have zero in
the denominator or a negative in a radical
-12
Check your solutions!
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SOLVE these Examples (dont forget to check
answers)
Check your solutions!
Check your solutions!
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SOLVE these Examples
x -3, -1
y3, -10
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SOLVE these Examples
X0, 3
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Hint for solving

• A quick way to solve a rational equation is to
  multiply everything through by the LCD.
• This will get rid of all the fractions!
• Beware of extraneous solutions!

This means check the solutions using the original
equations before you got rid of the fractions.
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Example Solve.
LCD 2x Multiply each fraction through by the LCD
Check your solution!
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Solve.
LCD ?
LCD (x1)
?
Check your solution!
No Solution!
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Recall Essential Question

• What is the difference between a rational
  expression and a rational equation?
• What is an extraneous solution?
• How do you check for extraneous solutions?

Equations have solutions
restriction on the domain
By plugging in your answers
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TOD SOLVE (dont forget to check answers)
X0, x-4/5