Chapter 4.2, Problem 46PS

### 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 13-50, perform the indicated operations involving rational expressions. Express final answers in simplest form.(Objective 2, 4, and 5) x y + x c + a y + a c x y − 2 x c + a y − 2 a c ⋅ 2 x 3 − 8 x 12 x 3 + 20 x 2 − 8 x

To determine

To perform:

The given operation and reduce it in simplest form.

Explanation

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, y do not assume values such that q(x,y)=0.

If ab and cd are rational numbers or expression, then the rational multiplication is formed by writing the numerator as product of numerators and denominator of the product as product of the denominator.

abâ‹…cd=aâ‹…cbâ‹…d=acbd

If m and k are nonzero integers and n is any integer, then the two fractions nâ‹…kmâ‹…k and nm follow the fundamental principle of fractions as given below.

nâ‹…kmâ‹…k=nm.

Calculation:

The given rational expression is xy+xc+ay+acxyâˆ’2xc+ayâˆ’2acâ‹…2x3âˆ’8x12x3+20x2âˆ’8x.

Use rational multiplication and factorization to simplify the given expression.

xy+xc+ay+acxyâˆ’2xc+ayâˆ’2acâ‹…2x3âˆ’8x12x3+20x2âˆ’8x=(xy+xc+ay+ac)(2x3âˆ’8x)(xyâˆ’2xc+ayâˆ’2ac)4x(3x2+5xâˆ’2)={x(y+c)+a(y+c)}2x(x2âˆ’4){x(yâˆ’2c)+a(yâˆ’2c)}4x(3x2+6

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