   Chapter 4.4, Problem 7PS

Chapter
Section
Textbook Problem

For Problems 1-40, perform the indicated operations, and express your answers in simplest form. (Objective 1) 6 a + 4 a 2 − 1 − 5 a − 1

To determine

To Find:

The simplest expression of 6a+4a215a1.

Explanation

Approach:

The expression of a rational 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 such that the variable x does not assume values such that q(x)=0.

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

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

Calculation:

The given expression is 6a+4a215a1.

Factorise the terms,

6a+4a215a1=6a+4(a1)(a+1)5(a1)

The LCD of the denominator is (a1)(a+1) where a1ora1

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