   Chapter 4.4, Problem 16PS

Chapter
Section
Textbook Problem

For Problems 1-40, perform the indicated operations, and express your answers in simplest form. (Objective 1) 6 a 2 − 3 a − 54 − 10 a 2 + 5 a − 6

To determine

To Find:

The simplest expression of 6a23a5410a2+5a6.

Explanation

Approach:

The rational expression is defined as the quotient obtained by a division of two polynomials in the form of p(x)q(x), where p(x) and q(x) are polynomials, while for any values of x the denominator q(x)0.

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

p(x)k(x)q(x)k(x)=p(x)q(x).

Calculation:

The given expression: 6a23a5410a2+5a6.

Factorise the terms.

6a23a5410a2+5a6=6a29a+6a5410a2+6aa6=6a(a9)+6(a9)10a(a+6)1(a+6)=6(a+6)(a9)10(a1)(a+6)

The LCD of the denominator is (a+6)(a9)(a1) where a6,a9ora1

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