soluzione


Calcolare

(1 - 18

x2 + 9
) · ( x

x2 - x - 6
+ x

x2 + 5x + 6
  -   1

x + 2
) : ( 1

x + 2
+ 1

x - 1
) =


= (1 - 18

x2 + 9
) · ( x

(x + 2)(x - 3)
+ x

(x + 2)(x + 3)
  -   1

x + 2
) : ( 1

x + 2
+ 1

x - 1
) =


= x2 + 9 - 18

x2 + 9
· x(x + 3) + x(x - 3) - (x - 3)(x + 3)

(x + 2)(x - 3)(x + 3)
: x - 1 + x + 2

x + 2
=


= x2 + 9 - 18

x2 + 9
· x2 + 3x + x2 - 3x - x2 + 9

(x + 2)(x - 3)(x + 3)
: x - 1 + x + 2

x + 2
=


= x2 - 9

x2 + 9
· x2 + 9

(x + 2)(x - 3)(x + 3)
: 2x + 1

x + 2
=


= x2 - 9

x2 + 9
· x2 + 9

(x + 2)(x - 3)(x + 3)
· x + 2

2x + 1
=


= (x - 3)(x + 3)

x2 + 9
· x2 + 9

(x + 2)(x - 3)(x + 3)
· x + 2

2x + 1
=


= 1

2x + 1