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 26E
To determine

To calculate: The product of the rational expression,

  x2+2x3x22x33x3+x

Expert Solution

Answer to Problem 26E

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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