Explanation Given: x 2 − x + 3 x 2 ( x − 1 ) Concept Used: To convert a complicated single fraction in partial fraction decomposition we follow the steps Factor the denominator completely into linear factors of the form ( a x + b ) m and quadratic factors of the form ( a x 2 + b x + c ) n that are not further factorable over the integers Set up the decomposition. That is, write the original rational expression as a sum of simpler fraction, as A 1 ( a x + b ) 1 + A 2 ( a x + b ) 2 + ......... + A m ( a x + b ) m , where A 1 , A 2 .... A m are constants And then solve to find the value of these constants For a first-degree (linear) denominator, the numerator is constant (degree 0) For a second-degree (linear) denominator, the numerator is linear (degree 1) Calculation: To set up partial fraction form for x 2 − x + 3 x 2 ( x − 1 ) First, break up the denominator into parts, as x 2 − x + 3 x 2 ( x − 1 ) = A x + B x 2 + C x − 1 Now we have to solve value of A, B, and C, as x 2 − x + 3 x 2 ( x − 1 ) = A x + B

Calculus: Special Edition: Chapters 1-5 (w/ WebAssign)

6th Edition

ISBN: 9781524908102

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.

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Chapter 7.4, Problem 6PS

To determine

Find the partial fraction decomposition for

x2−x+3x2(x−1).

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Chapter 7.4, Problem 5PS

Chapter 7.4, Problem 7PS

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Chapter 7 Solutions

Calculus: Special Edition: Chapters 1-5 (w/ WebAssign)

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Find the partial fraction decomposition for x 2 − x + 3 x 2 ( x − 1 ) .

Solution Summary: The author explains how to convert a complicated single tion in partial tion decomposition by dividing the denominator into linear and quadratic factors.

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Find the partial fraction decomposition for

x2−x+3x2(x−1).

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Chapter 7 Solutions

Find the partial fraction decomposition for x 2 − x + 3 x 2 ( x − 1 ) .

Solution Summary: The author explains how to convert a complicated single tion in partial tion decomposition by dividing the denominator into linear and quadratic factors.

Concept explainers

Videos

Find the partial fraction decomposition for x2−x+3x2(x−1).

Want to see the full answer?

Chapter 7 Solutions

Find the partial fraction decomposition for

x2−x+3x2(x−1).