# The simplified form the expression, x − 2 x 2 − 4 .

### 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 15E
To determine

## To calculate: The simplified form the expression, x−2x2−4 .

Expert Solution

The simplified form of the expression is 1x+2 .

### Explanation of Solution

Given information:

The expression x2x24 .

Formula used:

The algebraic identity: a2b2=(ab)(a+b) .

Calculation:

Consider the expression, x2x24 .

Rewrite the denominator in the form, a2b2 .

x2x24=x2(x2)(22)

Apply the algebraic identity, a2b2=(ab)(a+b) ,

x2x24=x2(x2)(22)=x2(x2)(x+2)

Strike off the common term,

x2x24=x2(x2)(22)=x2(x2)(x+2)=1(x+2)

The above expression can’t be simplified further.

Thus, the simplified form of the expression is 1x+2 .

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