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Chapter 7: Q. 7.37 (page 662)

Subtract:

2xx2-4-1x+2

Short Answer

Expert verified

The required result is1x-2.

Step by step solution

01

Step 1. Given information

The given expression is2xx2-4-1x+2.

02

Step 2. Find the LCD

  • Factor the denominator of the first rational expressions.

x2-4=x-2x+2

  • So, the LCD isx-2x+2.
03

Step 3. Express the expression with LCD  

  • Express the expression with LCD .

2xx2-4=2xx-2x+21x+2=x-2x-2x+2

04

Step 4. Subtract the obtained Expressions 

  • Subtract the obtained equivalent expressions and simplify by canceling out the common terms in numerator and denominator.

2xx-2x+2-x-2x-2x+2=2x-x+2x-2x+2=x+2x-2x+2=1x-2

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