Rational Expressions: (1/2x) + (4x/x^2 - 1) - (2/x+1)

Question

anonymous · Answer

you need to find the lcm of 2x, (x^2-1) and x+ 1

anonymous · Answer

first factor x^2-1
can you do this?

anonymous · Answer

no?

anonymous · Answer

i'm assuming you want to simplify this expression right?

4meisu · Answer

yes i do

4meisu · Answer

so the factor of x^2-1 will be (x-1) (x) ?

anonymous · Answer

x^2 - 1  this is 'difference' of two squares'  
= (x+1)(x-1)

and the lcm = 2x(x+1)(x-1)

anonymous · Answer

now we multiply each of three expressions by lcm and obtain:

(x+1)(x-1) +4x*2x - 2(x-1)
------------------------
        2x(x^2-1)

whats left to do is simplify the top of the fraction

4meisu · Answer

thanks, my teacher didn't explain this concept well at all...

anonymous · Answer

sorry i made a slight error 
correct is
(x+1)(x-1) +4x*2x - 4x(x-1)
------------------------
         2x(x^2-1)

=  5x^2 + 4x -1
    ------------
        2x(x^2-1)

= (5x  - 1 )(x  +1)
     -----------
     2x(x+1)(x-1)


=  5x-1
   -----
  2x(x-1)

4meisu · Answer

Wouldn't you factorize 5x^2 + 4x - 1 as (5x-1) (x+5) though?