Question

Efectuati:
$a) \frac{x}{2x+1} + \frac{2}{2x-1} - \frac{3x+1}{4 x^{2} -1}$

Answer 1

[  x ·( 2x -1)   + 2 ·( 2x + 1) - 3x -1 ]  /  ( 4x²  -1) = 
 = [ 2x²  -x + 4x + 2  -3x -1  ]  /   ( 4x² -1) = 
 = [ 2x² + 1 ] /   ( 2x -1 ) ·( 2x +1)

Answer 2

$\displaystyle \frac{x}{2x+1} + \frac{2}{2x-1} - \frac{3x+1}{4x^2-1} = \frac{x}{2x+1} + \frac{2}{2x-1}- \frac{3x+1}{(2x-1)(2x+1)} = \\ \\ = \frac{x(2x-1)+2(2x+1)-3x-1}{(2x-1)(2x+1)} = \frac{2x^2-x+4x+2-3x-1}{(2x-1)(2x+1)} = \\ \\ = \frac{2x^2+1}{(2x-1)(2x+1)}$