Solving Rational Equations- Formal Doodle Notes

Solving Rational Equations

Denominators are the same

Denominators can be made the same easily

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Solve with Proportions and Cross Products

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Rewrite so all parts have common denominator

Remember Domain Restrictions

​Domain Restrictions:
Set denominators = to 0 and solve.

Multiple Choice

Solve!

• x = 2
• x = 6
• x = 4
• x = 8

Multiple Choice

Solve the equation for x.

• 6
• 12
• 0
• 3

Multiple Choice

Which of the following below would be an extraneous solution to the equation?

• $$x\ =\ 3$$

• $$x\ =\ 5$$

• $$x\ =\ 1$$

• $$x\ =\ -5$$

Multiple Choice

Solve: $$\frac{3}{x-5}-\frac{20}{x^2-25}=\frac{2}{x+5}$$  

• $$x=-5$$  

• $$x=5$$  

• $$\frac{5}{\left(x+5\right)\left(x-5\right)}$$  

• No Solution

Multiple Choice

How do you know when a solution is extraneous?

• When you plug in the solution, there is 0 in a numerator.

• When you plug in the solution, there is 0 in a denominator.

• When the solution is x = 0

• It looks extra. 💁‍♀️

Multiple Choice

Which of the following below would be an extraneous solution to the equation?

• $$x\ =\ 2$$

• $$x\ =\ 7$$

• $$x\ =\ 14$$

• $$x\ =\ -2$$

Multiple Choice

Solve

• x = 7

• x = -3

• x = 2

• x = -2

Multiple Choice

Rational Functions have both a numerator a denominator

• False.
• True
• Rational Functions have only a numerator.
• Rational Functions have only a denominator.

Multiple Choice

Solve.

• x=2

• x= -2

• x=11

• x=22

Multiple Choice

Which of the following below would be an extraneous solution to the equation?

• $$x\ =\ 9$$

• $$x\ =\ -3$$

• $$x\ =\ -9$$

• $$x\ =\ 1$$