Chapter 4.2, Problem 47PS

### 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 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:

abâ‹…cd=aâ‹…cbâ‹…d=acbd

And the rational division:

If m and k are integers but not zero and n is any integer, then the two fractions nâ‹…kmâ‹…k and nm follow the fractionâ€™s fundamental principle as given below.

nâ‹…kmâ‹…k=nm.

Calculation:

The given rational expression is x2âˆ’x4yâ‹…10xy22xâˆ’2Ã·3x2+3x15x2y2.

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

x2âˆ’x4yâ‹…10xy22xâˆ’2Ã·3x2+3x15x2y2=x2âˆ’x4yâ‹…10xy22x

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