# The product of the rational expression, x 2 − x − 6 x 2 + 2 x ⋅ x 3 + x 2 x 2 − 2 x − 3 ### 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 28E
To determine

## To calculate: The product of the rational expression,  x2−x−6x2+2x⋅x3+x2x2−2x−3

Expert Solution

The product of rational expression is (x+3)x(x+2)

### Explanation of Solution

Given information:

The expression is given as:

x2x6x2+2xx3+x2x22x3

Formula used:

For the rational expression:

Fractions property:

ABCD=ACBD

Factoring trinomials: The factor of rational expression 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

x2x6x2+2xx3+x2x22x3

Use the fraction property for multiplying rational expression,

ABCD=ACBD

(x2x6)(x3+x2)(x2+2x)(x22x3)

Factor the first term in numerator byFactoring trinomials rule and common x2 from the second term,

(x23x+2x6)x2(x+1)(x2+2x)(x22x3)(x+3)(x3)x2(x+1)(x2+2x)(x22x3)

Factor the second term in denominator and common x from the first term,

(x+3)(x3)x2(x+1)x(x+2)(x23x+1x3)(x+3)(x3)x2(x+1)x(x+2)(x3)(x+1)

Cancel common factors from the numerators and denominator,

(x+3)x(x+2)

Thus, the product of rational expression is (x+3)x(x+2)

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