Chapter 4.1, Problem 41PS

Intermediate Algebra

10th Edition
Jerome E. Kaufmann + 1 other
ISBN: 9781285195728

Chapter
Section

Intermediate Algebra

10th Edition
Jerome E. Kaufmann + 1 other
ISBN: 9781285195728
Textbook Problem

For Problems 9-50, simplify each rational expression. (Objective 2) 4 x 2 y + 8 x y 2 − 12 y 3 18 x 3 y − 12 x 2 y 2 − 6 x y 3

To determine

To Find:

The expression by simplifying the given rational expression.

Explanation

Approach:

A rational expression is defined as the quotient obtained by a division of two polynomials in the form of p(x,y)q(x,y) where p(x,y) and q(x,y) are polynomials in such a way that the variables x and y do not assume values such that q(x,y)=0.

For values of x and y where q(x,y) and k(x,y) are both nonzero expressions, then by the fundamental principle of fractions, for all polynomials p(x,y), the following holds.

p(x,y)â‹…k(x,y)q(x,y)â‹…k(x,y)=p(x,y)q(x,y).

Calculation:

The given rational expression is 4x2y+8xy2âˆ’12y318x3yâˆ’12x2y2âˆ’6xy3.

Factorise the numerator 4x2y+8xy2âˆ’12y3.

4x2y+8xy2âˆ’12y3=4y(x2+2xyâˆ’3y2)=4y(x2+3xyâˆ’xyâˆ’3y2)=4y{x(x+3y)âˆ’y(x+3y)}=4y(xâˆ’y)(x+3y)

Factorise the denominator 18x3yâˆ’12x2y2âˆ’6xy3.

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