Answer t 2 + t + 2 ( t − 4 ) ( t + 4 ) Explanation Given: Expression: t t − 2 − 1 t + 2 Concept used: To simplify the given expression: Find the Least Common Multiple of the fraction and write in reduced form. Take out common terms in the given expression. Cancel out the terms that are in common in numerator and the denominator. Find if any algebraic identities can simplify the given expression. Calculation: Using the above concept, ⇒ t t − 2 − 1 t + 2 ⇒ t ( t + 2 ) − 1 ( t − 2 ) ( t − 2 ) ( t + 2 ) Take out the common terms in the numerator and denominator. ⇒ t ( t + 2 ) − 1 ( t − 2 ) ( t − 2 ) ( t + 2 ) ⇒ t ( t + 2 ) − 1 ( t − 2 ) ( t − 2 ) ( t + 2 ) ⇒ t 2 + 2 t − t + 2 t 2 + 2 t − 2 t − 4 ⇒ t 2 + t + 2 t 2 − 4 Consider the denominator, ⇒ t 2 − 4 ⇒ ( t − 4 ) ( t + 4 ) Substitute in the denominator, ⇒ t 2 + t + 2 ( t − 4 ) ( t + 4 ) Conclusion: Therefore, the simplified form of the expression is t 2 + t + 2 ( t − 4 ) ( t + 4 ) .

Algebra and Trigonometry: Structure and Method, Book 2

2000th Edition

ISBN: 9780395977255

Author: MCDOUGAL LITTEL

Publisher: McDougal Littell

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Question

Chapter 5.7, Problem 4MRE

To determine

To simplify the given expression.

Expert Solution & Answer

Answer to Problem 4MRE

t2+t+2(t−4)(t+4)

Explanation of Solution

Given:

Expression: tt−2−1t+2

Concept used:

To simplify the given expression:

Find the Least Common Multiple of the fraction and write in reduced form.
Take out common terms in the given expression.
Cancel out the terms that are in common in numerator and the denominator.
Find if any algebraic identities can simplify the given expression.

Calculation:

Using the above concept,

⇒tt−2−1t+2⇒t(t+2)−1(t−2)(t−2)(t+2)

Take out the common terms in the numerator and denominator.

⇒t(t+2)−1(t−2)(t−2)(t+2)⇒t(t+2)−1(t−2)(t−2)(t+2)⇒t2+2t−t+2t2+2t−2t−4⇒t2+t+2t2−4

Consider the denominator,

⇒t2−4⇒(t−4)(t+4)

Substitute in the denominator,

⇒t2+t+2(t−4)(t+4)

Conclusion:

Therefore, the simplified form of the expression is t2+t+2(t−4)(t+4).

Chapter 5.7, Problem 3MRE

Chapter 5.7, Problem 5MRE

Chapter 5 Solutions

Algebra and Trigonometry: Structure and Method, Book 2

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