# The product of the rational expression, x 2 − 2 x − 15 x 2 − 9 ⋅ x + 3 x − 5 ### 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 25E
To determine

## To calculate: The product of the rational expression,  x2−2x−15x2−9⋅x+3x−5

Expert Solution

The product of rational expression is (x+3)(x3) .

### Explanation of Solution

Given information:

The expression is given as:

x22x15x29x+3x5

Formula used:

For the rational expression:

Fractions property for multiplying rational expression:

ABCD=ACBD

Product formula: (A+B)(AB)=A2B2

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

x22x15x29x+3x5

Use the fraction property,

ABCD=ACBD

(x22x15)(x+3)(x29)(x5)

Factor the first term in numeratorbyFactoring trinomials method,

(x25x+3x15)(x+3)(x29)(x5)(x5)(x+3)(x+3)(x29)(x5)

Apply the product formula in denominator term,

(x5)(x+3)(x+3)(x3)(x+3)(x5)

Cancel common factors from the numerator and denominator,

(x+3)(x3)

Thus, the product of rational expression is (x+3)(x3)

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