# The division of the rational expression, 2 x + 1 2 x 2 + x − 15 ÷ 6 x 2 − x − 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 32E
To determine

## To calculate: The division of the rational expression,  2x+12x2+x−15÷6x2−x−2x+3

Expert Solution

The division of rational expression is 1(2x5)(3x2)

### Explanation of Solution

Given information:

The expression is given as:

2x+12x2+x15÷6x2x2x+3

Formula used:

For the rational expression:

Fractions property for dividing rational expression:

AB÷CD=ABDC

Fractions property for multiplying rational expression:

ABCD=ACBD

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

Factoring trinomials: The factor of algebraic 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, algebraic expression

2x+12x2+x15÷6x2x2x+3

Use the fraction property for dividing rational expression

AB÷CD=ABDC

2x+12x2+x15÷6x2x2x+3=2x+12x2+x15x+36x2x2

Use the fraction property for multiplying rational expression

ABCD=ACBD

(2x+1)(x+3)(2x2+x15)(6x2x2)

Factor the second term in denominator by Factoring trinomials rule,

(2x+1)(x+3)(2x2+6x5x15)(6x24x+3x2)(2x+1)(x+3)(x+3)(2x5)(3x2)(2x+1)

Cancel the common factors from the numerator and denominator,

1(2x5)(3x2)

Thus, the division of rational expression is 1(2x5)(3x2)

### Have a homework question?

Subscribe to bartleby learn! Ask subject matter experts 30 homework questions each month. Plus, you’ll have access to millions of step-by-step textbook answers!