Partial Fractions Decomposition

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Presentation transcript:

Partial Fractions Decomposition Section 7.4 Precalculus PreAP/Dual, Revised ©2018 Viet.dang@humbleisd.net 2/28/2019 1:06 PM §7.4: Partial Fractions Decomposition

§7.4: Partial Fractions Decomposition Definitions Consider adding two algebraic fractions Partial fraction decomposition reverses the process 2/28/2019 1:06 PM §7.4: Partial Fractions Decomposition

§7.4: Partial Fractions Decomposition Review Solve 𝟑 𝒙−𝟑 − 𝟐 𝒙−𝟐 2/28/2019 1:06 PM §7.4: Partial Fractions Decomposition

§7.4: Partial Fractions Decomposition Steps Factor the denominator and exclude any repeating denominators Separate the numerator by establishing 𝑨, 𝑩, etc… Plug in missing values to solve 2/28/2019 1:06 PM §7.4: Partial Fractions Decomposition

§7.4: Partial Fractions Decomposition Example 1 Write the partial fraction decomposition of 𝒙 𝒙 𝟐 −𝟓𝒙+𝟔 2/28/2019 1:06 PM §7.4: Partial Fractions Decomposition

§7.4: Partial Fractions Decomposition Example 1 Write the partial fraction decomposition of 𝒙 𝒙 𝟐 −𝟓𝒙+𝟔 2/28/2019 1:06 PM §7.4: Partial Fractions Decomposition

§7.4: Partial Fractions Decomposition Example 2 Write the partial fraction decomposition of 𝒙+𝟕 𝒙 𝟐 −𝒙−𝟔 2/28/2019 1:06 PM §7.4: Partial Fractions Decomposition

§7.4: Partial Fractions Decomposition Your Turn Write the partial fraction decomposition of 𝟐 𝒙 𝟐 −𝟏 2/28/2019 1:06 PM §7.4: Partial Fractions Decomposition

§7.4: Partial Fractions Decomposition Process Given 𝒇 𝒙 = 𝑷(𝒙 𝒙−𝒓 𝒏 Where polynomial 𝑷 𝒙 has degree < 𝒏 𝑷 𝒓 ≠𝟎 B. Then 𝒇 𝒙 can be decomposed with this cascading form 2/28/2019 1:06 PM §7.4: Partial Fractions Decomposition

§7.4: Partial Fractions Decomposition Example 3 Write the partial fraction decomposition of 𝒙+𝟐 𝒙 𝟑 −𝟐 𝒙 𝟐 +𝒙 2/28/2019 1:06 PM §7.4: Partial Fractions Decomposition

§7.4: Partial Fractions Decomposition Example 3 Write the partial fraction decomposition of 𝒙+𝟐 𝒙 𝟑 −𝟐 𝒙 𝟐 +𝒙 2/28/2019 1:06 PM §7.4: Partial Fractions Decomposition

§7.4: Partial Fractions Decomposition Example 4 Write the partial fraction decomposition of 𝟕𝒙 𝟐 +𝟓𝒙+𝟐𝟑 𝒙+𝟏 𝒙 𝟐 +𝟒 2/28/2019 1:06 PM §7.4: Partial Fractions Decomposition

§7.4: Partial Fractions Decomposition Example 4 Write the partial fraction decomposition of 𝟕𝒙 𝟐 +𝟓𝒙+𝟐𝟑 𝒙+𝟏 𝒙 𝟐 +𝟒 2/28/2019 1:06 PM §7.4: Partial Fractions Decomposition

§7.4: Partial Fractions Decomposition Your Turn Write the partial fraction decomposition of 𝒙 𝟐 −𝒙+𝟐 𝒙 𝒙+𝟐 𝟐 2/28/2019 1:06 PM §7.4: Partial Fractions Decomposition

§7.4: Partial Fractions Decomposition Assignment Page 506 5-8 all, 17-29 odd 2/28/2019 1:06 PM §7.4: Partial Fractions Decomposition