2x/x^2-3x + 2x/x^2-4x+3 + x/x-1

`A = ( 2x ) / ( x^2 - 3x ) + ( 2x ) / ( x^2 - 4x + 3 ) + x / ( x - 1 )` `( x \ne 0 ; x \ne 1 ; x \ne 3 )`

$\\$ `= ( 2x ) / [ x ( x - 3 ) ] + ( 2x ) / [ ( x - 1 ) ( x - 3 ) ] + x / ( x - 1 )`

$\\$ `= [ 2x ( x - 1 ) + 2x^2 + x^2 ( x - 3 ) ] / [ x ( x - 3 ) ( x - 1 ) ]`

$\\$ `= ( 2x^2 - 2x + 2x^2 + x^3 - 3x^2 ) / [ x ( x - 3 ) ( x - 1 ) ]`

$\\$ `= ( x^3 + x^2 - 2x ) / [ x ( x - 3 ) ( x - 1 ) ]`

$\\$ `= [ x ( x - 1 ) ( x + 2 ) ] / [ x ( x - 3 ) ( x - 1 ) ]`

$\\$ `= ( x + 2 ) / ( x - 3 )`