Methods for Solving Rational Equations

What is the purpose of partial fraction decomposition?

• To make rational functions more difficult to solve

• The purpose of partial fraction decomposition is to simplify and solve rational functions by breaking them down into simpler fractions.

• To complicate and confuse rational functions

• To add unnecessary steps to solving rational functions

What are the steps involved in solving partial fraction decomposition problems?

• Add the constants for each factor and then factor the denominator

• Divide the numerator by the denominator

• Multiply the denominator by a random number

• Identify the denominator, factor it into linear and irreducible quadratic factors, and then use the method of undetermined coefficients to find the constants for each factor.

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CCSS.HSA.APR.D.7

How do you determine the unknown coefficients in partial fraction decomposition?

• By asking a friend for the coefficients

• By using a magic 8-ball

• By equating the given rational function to the sum of its partial fractions and solving for the unknown coefficients.

• By flipping a coin and guessing

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CCSS.HSA.APR.D.6

How do you apply partial fraction decomposition in real-life scenarios?

• Partial fraction decomposition can be used in engineering, physics, and economics to simplify complex equations and make them easier to solve.

• Partial fraction decomposition is used in cooking to create new recipes

• Partial fraction decomposition is applied in agriculture to improve crop yield

• Partial fraction decomposition is used in fashion design to create new clothing patterns

Solve and check for extraneous solutions

• x=7 & -2 is extraneous 

• x= -2 and 7 is extraneous

• No Solution

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CCSS.HSA.REI.A.2

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CCSS.HSA.REI.A.2

Solve for v

• - 7/6

• - 9/5

• 9/5

• -3

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CCSS.HSA.REI.A.2

Solve for x:
x/32.4=22

x=_

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CCSS.6.EE.B.7

Solve for r

Mathematical Equivalence

ON

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CCSS.HSA.REI.A.2

What is the first step in partial fraction decomposition?

• Find the common denominator of the fractions

• Add the numerators of the partial fractions

• Identify the denominator and factor it into its irreducible factors.

• Multiply the numerator and denominator by a common factor

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CCSS.HSA.APR.D.6