Explanation Given: The rational expression is, z 2 − 5 z + 6 z 2 − 4 . Property used: Fundamental property, P Q = P S Q S , for all mathematical expressions P , Q , R , and S , with Q ≠ 0 and S ≠ 0 . Calculation: Factorise the numerator, z 2 − 5 z + 6 of the given rational expression. z 2 − 5 z + 6 = z 2 − 2 z − 3 z + 6 = z ( z − 2 ) − 3 ( z − 2 ) = ( z − 2 ) ( z − 3 ) Factorise the numerator, z 2 − 4 of the given rational expression. z 2 − 4 = ( z ) 2 − ( 2 ) 2 [ Difference of two squares, x 2 − y 2 = ( x + y ) ( x − y ) ] = ( z + 2 ) ( z − 2 ) Thus, the rational expression becomes, z 2 − 5 z + 6 z 2 − 4 = ( z − 2 ) ( z − 3 ) ( z + 2 ) ( z − 2 ) Apply the fundamental property of rational expression, P Q = P S Q S

Calculus with Applications (11th Edition)

11th Edition

ISBN: 9780321979421

Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Publisher: PEARSON

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Chapter R.3, Problem 10E

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To express: The rational expression z2−5z+6z2−4 in lowest terms.

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Chapter R.3, Problem 9E

Chapter R.3, Problem 11E

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Calculus with Applications (11th Edition)

Ch. R.1 - YOUR TURN 1 Perform the operation Ch. R.1 - YOUR TURN 2 Perform the operation . Ch. R.1 - Prob. 3YT Ch. R.1 - Prob. 4YT Ch. R.1 - Perform the indicated operations. 1. Ch. R.1 - Prob. 2E Ch. R.1 - Prob. 3E Ch. R.1 - Prob. 4E Ch. R.1 - Perform the indicated operations. 5. Ch. R.1 - Perform the indicated operations. 6.

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To express: The rational expression z 2 − 5 z + 6 z 2 − 4 in lowest terms.

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To express: The rational expression z2−5z+6z2−4 in lowest terms.

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Chapter R Solutions