Explanation A rational expression is defined as the quotient obtained by a division of two polynomials in the form of p ( a ) q ( a ) where p ( a ) and q ( a ) are polynomials in such a way that the variable a does not assume values such that q ( a ) = 0 . For values of a , where q ( a ) and k ( a ) are both nonzero expressions, then by the fundamental principle of fractions, for all polynomials p ( a ) , the following holds. p ( a ) ⋅ k ( a ) q ( a ) ⋅ k ( a ) = p ( a ) q ( a ) . Calculation: The given rational expression is a 2 + 4 a − 32 3 a 2 + 26 a + 16 . Factorise the numerator a 2 + 4 a − 32 . a 2 + 4 a − 32 = a 2 + 8 a − 4 a − 32 = a ( a + 8 ) − 4 ( a + 8 ) = ( a − 4 ) ( a + 8 ) Factorise the denominator 3 a 2 + 26 a + 16

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ISBN: 9781305191495

Author: Jerome E. Kaufmann; Karen L. Schwitters

Publisher: Cengage Learning US

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Chapter 4.1, Problem 24PS

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The expression by simplifying the given rational expression.

Solution Summary: The author explains that a rational expression is defined as the quotient obtained by division of two polynomials.

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To Find:

The expression by simplifying the given rational expression.