Chapter 4.S, Problem 1S

### 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

# Simplify x 2 − 3 x − 10 x 2 + 9 x + 14 .

To determine

To Find:

The expression by simplifying the given rational expression x23x10x2+9x+14.

Explanation

Approach:

A rational expression is defined as the quotient obtained by a division of two polynomials in the form of p(a)q(a) where p(a) and q(a) are polynomials in such a way that the variable a does not assume values such that q(a)=0.

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

p(a)â‹…k(a)q(a)â‹…k(a)=p(a)q(a).

Calculation:

The given rational expression is x2âˆ’3xâˆ’10x2+9x+14.

Factorise the numerator x2âˆ’3xâˆ’10.

x2âˆ’3xâˆ’10=x2âˆ’5x+2xâˆ’10=x(xâˆ’5)+2(xâˆ’5)=(xâˆ’5)(x+2)

Factorise the denominator x2+9x+14

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