# The product of the rational expression, t − 3 t 2 + 9 ⋅ t + 3 t 2 − 9

### 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 27E
To determine

## To calculate: The product of the rational expression,  t−3t2+9⋅t+3t2−9

Expert Solution

The product of rational expression is 1(t2+9)

### Explanation of Solution

Given information:

The expression is given as:

t3t2+9t+3t29

Formula used:

For the rational expression:

Fractions property for the multiplying rational expression:

ABCD=ACBD

Product formula: (A+B)(AB)=A2B2

Calculation:

Consider the, rational expression

t3t2+9t+3t29

Use the fraction property for multiplying the rational expression,

ABCD=ACBD

(t3)(t+3)(t2+9)(t29)

Factor the denominator by product rule,

(t3)(t+3)(t2+9)(t3)(t+3)

Cancel the common factors from the numerator and denominator,

1(t2+9)

Thus, the product of rational expression is 1(t2+9)

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