# Thesimplified form of the expression 2 + x x + 3

### 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 39E
To determine

## To calculate:Thesimplified form of the expression 2+xx+3

Expert Solution

The simplified form of the expression is 3(x+2)x+3_

### Explanation of Solution

Given information:

The expression is 2+xx+3

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 the 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. 2+xx+3

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.

Re-write the given expression as:

21+xx+3

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

The least common denominator of 1 and (x+3) is (x+3) .

21+xx+3=2(x+3)1(x+3)+x(x+3)

21+xx+3=2×(x+3)+x×1(x+3)=2x+6+x(x+3)

Combine terms in numerator,

21+xx+3=3x+6(x+3)

Factor out 3 from each term of numerator,

21+xx+3=3(x+2)(x+3)

Thus, the simplified form of the expression is 3(x+2)(x+3)

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