Chapter 4.4, Problem 34PS

### 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 1-40, perform the indicated operations, and express your answers in simplest form. (Objective 1) 2 x + 5 x 2 + 3 x − 18 − 3 x − 1 x 2 + 4 x − 12 + 5 x − 2

To determine

To Find:

The simplest expression of 2x+5x2+3x183x1x2+4x12+5x2.

Explanation

Approach:

If ab and cd are rational, then addition or subtraction of rational formed by multiplying them by appropriate expressions and equating the denominators using LCD and perform the operation as below:

And,

Same algebra is used for rational expression.

Calculation:

The given expression:2x+5x2+3xâˆ’18âˆ’3xâˆ’1x2+4xâˆ’12+5xâˆ’2.

Factorise the terms.

2x+5x2+3xâˆ’18âˆ’3xâˆ’1x2+4xâˆ’12+5xâˆ’2=2x+5x2+6xâˆ’3xâˆ’18âˆ’3xâˆ’1x2+6xâˆ’2xâˆ’12+5xâˆ’2=2x+5x(x+6)âˆ’3(x+6)âˆ’3xâˆ’1x(x+6)âˆ’2(x+6)+5xâˆ’2=2x+5(xâˆ’3)(x+6)âˆ’3xâˆ’1(xâˆ’2)(x+6)+5xâˆ’2

The LCD of the denominator is (xâˆ’2)(x+6)(xâˆ’3) where xâ‰ 3,xâ‰ 2â€‰orâ€‰xâ‰ âˆ’6

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