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Chapter 11: Q. 8 (page 765)

Tell whether the given rational expression is proper or improper. If improper, rewrite it as the sum of a polynomial and a proper rational expression.

3x2-2x2-1.

Short Answer

Expert verified

The rational expression 3x2-2x2-1is improper.

The sum of a polynomial and a proper rational expression is3+1x2-1.

Step by step solution

01

Step 1. Given Information.

The rational expression is,

3x2-2x2-1.

02

Step 2. Proper or Improper rational expression.

3x2-2x2-1

The degree of the numerator=2.

The degree of the denominator=2

The degree of the numerator=The degree of the denominator.

It is an improper rational expression.

03

Step 3. Sum of polynomial and Proper rational expression.

The improper rational expression is,

3x2-2x2-1

Add and subtract 1in the numerator,

=3x2-2+1-1x2-1=3x2-3+1x2-1=3x2-3x2-1+1x2-1=3(x2-1)x2-1+1x2-1=3+1x2-1

The polynomial is 3and the proper rational expression is1x2+1.

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