BuyFind

Precalculus: Mathematics for Calcu...

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

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+x15÷6x2x2x+3

Expert Solution

Answer to Problem 32E

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)

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