# The product of the rational expression, x 2 + 2 x − 3 x 2 − 2 x − 3 ⋅ 3 − x 3 + x ### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071 ### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 1.4, Problem 26E
To determine

## To calculate: The product of the rational expression,  x2+2x−3x2−2x−3⋅3−x3+x

Expert Solution

The product of rational expression is (x1)(x+1)

### Explanation of Solution

Given information:

The expression is given as:

x2+2x3x22x33x3+x

Formula used:

For the rational expression:

Fractions property:

ABCD=ACBD

Factoring trinomials: The factor of rationalexpression which contain three terms is of the from x2+bx+c ,

(x+r)(x+s)=x2+(r+s)x+rs

Choose the values of r and s which satisfied these equations r+s=b and rs=c

Calculation:

Consider the, rational expression

x2+2x3x22x33x3+x

Use the fraction property,

ABCD=ACBD

(x2+2x3)(3x)(x22x3)(3+x)

Factor the both numerator and denominator terms,

(x2+3x1x3)(3x)(x23x+1x3)(3+x)(x+3)(x1)(3x)(x3)(x+1)(3+x)

Common minus from the numerator,

(x+3)(x1)(x3)(x3)(x+1)(x+3)

Cancel common factors from the numerator and denominator,

(x1)(x+1)

Thus, the product of rational expression is (x1)(x+1)

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