( 3x ) / [ x2 + 2x + 1 ] = ( 3x ) / [ (x + 1)(x + 1) ]
( 2 ) / [ x2 - 1 ] = ( 2 ) / [ (x + 1)(x - 1) ]
The lowest common denominator is: (x + 1)(x + 1)(x - 1)
Multiplying the top fraction by (x - 1) / (x - 1):
( 3x ) / [ (x + 1)(x + 1) ] · (x - 1) / (x - 1) = [ (3x)(x - 1) ] / [ (x + 1)(x + 1)(x - 1) ] = [ 3x2 - 3x ] / / [ (x + 1)(x + 1)(x - 1) ]
Multiplying the bottom fraction by (x + 1) / (x + 1)
( 2 ) / [ (x + 1)(x - 1) ] · (x + 1) / (x + 1) = [ (2)(x + 1) ] / [ (x + 1)(x - 1)(x + 1) ] = [ 2x + 2 ] / [ (x + 1)(x + 1)(x - 1) ]
Subtracting the second from the first: [ 3x2 - 5x - 2 ] / [ (x + 1)(x + 1)(x - 1) ]