Show all work to simplify 2 over x + 2 over x plus 1 - 2 over x plus 2. Use complete sentences to explain how to simplify this expression. Remember to list all

Question

Show all work to simplify 2 over x + 2 over x plus 1 - 2 over x plus 2. Use complete sentences to explain how to simplify this expression. Remember to list all restrictions.

Answer 1

IF the problem is 2/(x + 2)    _        2       then you could make a

                               x + 1             x + 2  

 

common denominator of (x + 1)(x + 2). So to do that, you would have to multiply the left expression by (x + 2), and the right one by (x + 1).

 

Now we have    2(x+ 2)/(x + 2)  --  2(x + 1)   

                                 (x + 1)(x + 2)

 

This simplifies to        2 - 2x - 2        =            -2x         

                             (x + 1)(x + 2)               (x + 1)(x + 2)

 

 Restrictions: x cannot = -1, -2