# The rational expression x 2 + 3 x + 2 x 2 − x − 2 .

### Single Variable Calculus: Concepts...

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

### Single Variable Calculus: Concepts...

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

(a)

To determine

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

Expert Solution

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 2x2−x−1x2−9⋅x+32x+1.

Expert Solution

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 x2x2−4−x+1x+2.

Expert Solution

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 yx−xy1y−1x.

Expert Solution

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).

### 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!