Chapter 4.3, Problem 68PS

### 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

# Consider the addition problem 8 x − 2 + 5 2 − x . Note that the denominators are opposites of each other. If the property a − b = − a b is applied to the second fraction, we have 5 2 − x = − 5 x − 2 . Thus we proceed as follows: 8 x − 2 + 5 2 − x = 8 x − 2 − 5 x − 2 = 8 − 5 x − 2 = 3 x − 2 Use this approach to do the following problems.(a) 7 x − 1 + 2 1 − x (b) 5 2 x − 1 + 8 1 − 2 x (c) 4 a − 3 − 1 3 − a (d) 10 a − 9 − 5 9 − a (e) x 2 x − 1 − 2 x − 3 1 − x (f) x 2 x − 4 − 3 x − 28 4 − x

To determine

(a).

To solve:

The operation 7x1+21x.

Explanation

Approach:

A 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 in such a way 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 fundamental principle of fractions, for all polynomials p(x), the following holds.

p(x)â‹…k(x)q(x)â‹…k(x)=p(x)q(x)

To determine

(b).

To solve:

The operation 52x1+812x.

To determine

(c).

To solve:

The operation 4a313a.

To determine

(d).

To solve:

The operation 10a959a.

To determine

(e).

To solve:

The operation x2x12x31x.

To determine

(f).

To solve:

The operation x2x43x284x.

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