   Chapter 4.2, Problem 47PS

Chapter
Section
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 2 − x 4 y ⋅ 10 x y 2 2 x − 2 ÷ 3 x 2 + 3 x 15 x 2 y 2

To determine

To Perform:

The given operation and reduce it in simplest form.

Explanation

Concept:

Rational expression demarcate as a quotient obtained by a division of two polynomials in the form of p(x)q(x) where p(x) and q(x) are polynomials in such a way that the variable x does not assume values such that q(x)=0.

If ab and cd are rational numbers, then the rational multiplication:

abcd=acbd=acbd

And the rational division:

If m and k are integers but not zero and n is any integer, then the two fractions nkmk and nm follow the fraction’s fundamental principle as given below.

nkmk=nm.

Calculation:

The given rational expression is x2x4y10xy22x2÷3x2+3x15x2y2.

Use rational multiplication, division and factorization to simplify the given expression,

x2x4y10xy22x2÷3x2+3x15x2y2=x2x4y10xy22x

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