   Chapter 4.2, Problem 33PS

Chapter
Section
Textbook Problem

For Problems 13-50, perform the indicated operation involving rational expressions. Express final answers in simplest form. (Objective 2, 4 and 5) x 2 − 4 x y + 4 y 2 7 x y 2 ÷ 4 x 2 − 3 x y − 10 y 2 20 x 2 y + 25 x y 2

To determine

To Perform:

The given operation and reduce it in simplest form.

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

If ab and cd are rational numbers, then the rational division is formed by writing the numerator as the quotient of numerator of the first and denominator of the second rational numbers, and writing the denominator as the quotient of numerator of the first and denominator of the second rational numbers.

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

nkmk=nm.

Calculation:

The given rational expression is x24xy+4y27xy2÷4x23xy10y220x2y+25xy2.

Use rational division and factorization,

x24xy+4y27xy2÷4x23xy10y220x2y+25xy2=x24xy+4y27xy220x2y+25xy24x23xy10y2={(x)22(x)(2y)+(2y)2}5x

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