BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

Chapter T, Problem 5ADT

(a)

To determine

To simplify: The rational expression x2+3x+2x2x2.

Expert Solution

Answer to Problem 5ADT

The rational expression x2+3x+2x2x2 is simplified as 62.

Explanation of Solution

Consider the rational expression x2+3x+2x2x2.

Simplify the above expression as follows,

3(x+6)+4(2x5)=3x+3×6+4×2x4×5=3x+18+8x20=11x2

Thus, the rational expression x2+3x+2x2x2 is simplified as 11x2.

(b)

To determine

To simplify: The rational expression 2x2x1x29x+32x+1.

Expert Solution

Answer to Problem 5ADT

The rational expression 2x2x1x29x+32x+1 is simplified as x1x3.

Explanation of Solution

Consider the rational expression 2x2x1x29x+32x+1.

Simplify the above expression as follows,

2x2x1x29×x+32x+1=2x22x+x1x232×x+32x+1=2x(x1)+1(x1)(x+3)(x3)×x+32x+1(a2b2=(a+b)(ab))=(2x+1)(x1)(x+3)(x3)×x+32x+1=x1x3

Thus, the rational expression 2x2x1x29x+32x+1 is simplified as x1x3.

(c)

To determine

To simplify: The rational expression x2x24x+1x+2.

Expert Solution

Answer to Problem 5ADT

The rational expression x2x24x+1x+2 is simplified as 1x2.

Explanation of Solution

Consider the rational expression x2x24x+1x+2.

Simplify the above expression as follows,

x2x24x+1x+2=x2x222x+1x+2=x2(x+2)(x2)x+1x+2(a2b2=(a+b)(ab))=x2(x+1)(x2)(x+2)(x2)=x2(x22x+x2)(x+2)(x2)

On the further simplification the above expression becomes,

x2x24x+1x+2=x2x2+x+2(x+2)(x2)=x+2(x+2)(x2)=1x2

Thus, the rational expression x2x24x+1x+2 is simplified as 1x2.

(d)

To determine

To simplify: The rational expression yxxy1y1x.

Expert Solution

Answer to Problem 5ADT

The rational expression yxxy1y1x is simplified as 1x2.

Explanation of Solution

Consider the rational expression yxxy1y1x.

Simplify the above expression as follows,

yxxy1y1x=y2x2xyxyxy=(y+x)(yx)xyxyxy(a2b2=(a+b)(ab))=(y+x)(yx)xy×xyxy=(y+x)(yx)(yx)

=(x+y)

Thus, the rational expression yxxy1y1x is simplified as (x+y).

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