Chapter 4.7, Problem 1PS

### 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 1-30, solve each equation. (Objective 1) x 4 x − 4 + 5 x 2 − 1 = 1 4

To determine

To Solve:

The equation x4x4+5x21=14.

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).

Calculation:

The given rational expression is x4xâˆ’4+5x2âˆ’1=14.

Factorize each term of the equation,

x4xâˆ’4+5x2âˆ’1=14x4(xâˆ’1)+5(xâˆ’1)(x+1)=14

Restriction on the equation is that xâ‰ 1â€‰andâ€‰xâ‰ âˆ’1,

The lowest common denominator of the given equation is 4(xâˆ’1)(x+1)

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