Chapter 4.4, Problem 39PS

### Intermediate Algebra

10th Edition
Jerome E. Kaufmann + 1 other
ISBN: 9781285195728

Chapter
Section

### Intermediate Algebra

10th Edition
Jerome E. Kaufmann + 1 other
ISBN: 9781285195728
Textbook Problem

# For Problems 1-40, perform the indicated operations, and express your answers in simplest form. (Objective 1) t + 3 3 t − 1 + 8 t 2 + 8 t + 2 3 t 2 − 7 t + 2 − 2 t + 3 t − 2

To determine

To Find:

The simplest expression of t+33t1+8t2+8t+23t27t+22t+3t2.

Explanation

Approach:

Rational expression, a quotient obtained by division of two polynomials in form of p(x,y)q(x,y) where p(x,y) and q(x,y) are polynomials in such a way that the variables x,y do not assume values such that q(x,y)=0.

If ab and cd are rational, then addition or subtraction of rational formed by multiplying them by appropriate expressions and equating the denominators using LCD and perform the operation as below:

And,

Same algebra is used for rational expression.

Calculation:

The given expression:t+33tâˆ’1+8t2+8t+23t2âˆ’7t+2âˆ’2t+3tâˆ’2.

Factorise the terms.

t+33tâˆ’1+8t2+8t+23t2âˆ’7t+2âˆ’2t+3tâˆ’2=t+33tâˆ’1+8t2+8t+23t2âˆ’6tâˆ’t+2âˆ’2t+3tâˆ’2=t+33tâˆ’1+8t2+8t+2t(3tâˆ’1)âˆ’2(3tâˆ’1)âˆ’2t+3tâˆ’2=t+33tâˆ’1+8t2+8t+2(3tâˆ’1)(tâˆ’2)âˆ’2t+3tâˆ’2

The LCD of the denominator is (3tâˆ’1)(tâˆ’2) where tâ‰ 13â€‰orâ€‰tâ‰ 2.

Change each fraction into an equivalent fraction which has LCD as a denominator

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