# The rationalize expression 10 5 − 2 .

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

(a)

To determine

## To simplify: The rationalize expression 105−2.

Expert Solution

The rational expression 1052 is simplified as 52+210.

### Explanation of Solution

Consider the rational expression 1052.

Simplify the above expression as follows,

1052=1052×5+25+2=10×5+10×2(5)2(2)2((a+b)(ab)=a2b2)=50+21054=5×5×2+21054

=52+210

Thus, the rational expression 1052 is simplified as 52+210.

(b)

To determine

### To simplify: The rationalize expression 4+h−2h.

Expert Solution

The rational expression 4+h2h is simplified as 14+h+2.

### Explanation of Solution

Consider the rational expression 4+h2h.

Simplify the above expression as follows,

4+h2h=4+h2h×4+h+24+h+2=(4+h)2(2)2h(4+h+2)((a+b)(ab)=a2b2)=4+h4h(4+h+2)=hh(4+h+2)

=14+h+2

Thus, the rational expression 4+h2h is simplified as 14+h+2.

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