# The number of terms in the expression. ### 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 4E

(a)

To determine

## To find: The number of terms in the expression.

Expert Solution

The number of terms is 3 in the expression.

### Explanation of Solution

A polynomial with variable x is an expression of the form,

anxn+an1xn1++a1x+a0

Where,

• a is a real number.
• n is nonnegative integer.

The monomial anxn that combine together to make the polynomial are known as the terms of the polynomial.

The given expression is,

1x2x+1x(x+1)2

Thus, the number of terms is 3 in the expression.

(b)

To determine

### To find: The least common denominator of the terms.

Expert Solution

The least common denominator of all the terms is x(x+1)2 .

### Explanation of Solution

Given:

The given expression is,

1x2x+1x(x+1)2

Calculation:

Factor each denominator of given expression and take the product of distinct factors, than the highest power that appears in any of the factors is the least common denominator.

All the denominators of the expression are x, (x+1) and (x+1)2 . The least common denominator is x(x+1)2 .

Thus, the least common denominator of all the terms is x(x+1)2 .

(c)

To determine

### To find: The sum of given rational fractions.

Expert Solution

The sum of given rational fractions is 2x2+1x(x+1)2 .

### Explanation of Solution

Given:

The expression is,

1x2x+1x(x+1)2

Calculation:

Use least common denominator to add the given rational fractions.

1x2x+1x(x+1)2=(x+1)2x(x+1)22x(x+1)x(x+1)2x2x(x+1)2=x2+2x+1x(x+1)22x2+2xx(x+1)2x2x(x+1)2=x2+2x+12x22xx2x(x+1)2(Combinetermsinnumerator)=2x2+1x(x+1)2

Thus, the sum of given rational fractions is 2x2+1x(x+1)2 .

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