# The factor of the expression x − 1 / 2 ( x + 1 ) 1 / 2 + x 1 / 2 ( x + 1 ) − 1 / 2 .

### 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 1.3, Problem 94E
To determine

## To calculate: The factor of the expression x−1/2(x+1)1/2+x1/2(x+1)−1/2 .

Expert Solution

The factor of the expression x1/2(x+1)1/2+x1/2(x+1)1/2 is 1x2+x(2x+1) .

### Explanation of Solution

Given information:

The expression x1/2(x+1)1/2+x1/2(x+1)1/2 .

Formula used:

To factor an expression, split the terms in the expression into multiplication of simpler expressions, then take the common power out and group the expressions together.

Calculation:

Consider the given expression x1/2(x+1)1/2+x1/2(x+1)1/2 .

Recall that to factor an expression, split the terms in the expression into multiplication of simpler expressions, then take the common power out and group the expressions together.

The greatest common factor of these terms is x1/2(x+1)1/2 .

Apply it,

x1/2(x+1)1/2+x1/2(x+1)1/2=x1/2(x+1)1/2[(x+1)1/2(x+1)1/2+x1/2x1/2]=x1/2(x+1)1/2[(x+1)12+12+x12+12]=1xx+1[x+1+x]=1x2+x(2x+1)

Thus, the factor of expression x1/2(x+1)1/2+x1/2(x+1)1/2 is 1x2+x(2x+1) .

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