# Thesimplified form of the expression 1 x + 1 + 1 x − 1

### 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 42E
To determine

## To calculate:Thesimplified form of the expression 1x+1+1x−1

Expert Solution

The simplified form of the expression is 2xx21_

### Explanation of Solution

Given information:

The expression is 1x+1+1x1

Formula used:

To add or subtract rational expression, first find the common denominator and then use the following property of fractions:

PR+QR=P+QR

If denominators are not same then find least common denominator. The least common denominator is found factoring each denominator and taking the product of distinct factors, using the highest power that appears in any of the factors.

Calculation:

Consider the provided expression. 1x+1+1x1

Recall that,

To add or subtract rational expression, first find the common denominator and then use the following property of fractions:

PR+QR=P+QR

If denominators are not same then find least common denominator. The least common denominator is found factoring each denominator and taking the product of distinct factors, using the highest power that appears in any of the factors.

Since denominators are not the same then find the least common denominator.

The least common denominator of (x+1) and (x1) is (x+1)(x1)=x21 .

1x+1+1x1=1×(x1)(x+1)(x1)+1×(x+1)(x+1)(x1)

1x+1+1x1=1×(x1)+1×(x+1)(x+1)(x1)

Use algebraic identity,

1x+1+1x1=x1+x+1x21

Combine terms in numerator,

1x+1+1x1=2xx21

Thus, the simplified form of the expression is 2xx21

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