# To simplify 2 x + 1 x − 2 + 3 ( x − 2 ) 2 by using appropriate operations. ### 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, Problem 58RE
To determine

## To simplify 2x+1x−2+3(x−2)2 by using appropriate operations.

Expert Solution

### Explanation of Solution

Given information:

2x+1x2+3(x2)2

Formula used:

Properties of fractions:- AC+BC=A+BC

Difference of squares : A2B2=(AB)(A+B)

Calculations:

First Term 2x

Second Term 1x2

Now,

=2x+1x2

writing the fraction in LCD (least common denominator) form we have,

=2(x2)x(x2)+xx(x2)

=2x4+2x(x2)=2x2x(x2)

New term 2x2x(x2) (i)

Third term 3(x2)2  (ii)

Solving equation (i) and (ii)

=2x2x(x2)+3(x2)2

Taking 1(x2) common

=1(x2){2x2x+3(x2)}

writing the fraction in LCD (least common denominator) form we have,

=1(x2){(2x2)(x2)x(x2)+3xx(x2)}=1(x2){2x24x2x+4x(x2)+3xx(x2)}=1(x2){2x26x+4+3xx(x2)}=1(x2){2x23x+4x(x2)}

=2x23x+4x(x2)2

After simplifying we get 2x23x+4x(x2)2 .

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