# To simplify 1 x − 1 x + 1 1 x + 1 x + 1 by using appropriate operations.

### 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, Problem 62RE
To determine

## To simplify 1x−1x+11x+1x+1 by using appropriate operations.

Expert Solution

### Explanation of Solution

Given information:

1x1x+11x+1x+1

Formula used:

Properties of fractions:- ACBC=ABC

Properties of fractions :- AB÷CD=AB.DC

Calculations:

Numerator = 1x1x+1

Writing fraction in form of LCD (least common denominator)

=x+1x(x+1)xx(x+1)=x+1xx(x+1)=1x(x+1) (i)

Denominator = 1x+1x+1

Writing fraction in form of LCD (least common denominator)

=x+1x(x+1)+xx(x+1)=x+1+xx(x+1)=2x+1x(x+1)  (ii)

Now,

=1x(x+1)÷2x+1x(x+1)=1x(x+1).x(x+1)2x+1

=12x+1 ( by cancelling x(x+1) )

After simplifying we get 12x+1 .

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