I need a little bit of help here.

Question

x(x-1)+(x-1)(x+2)
_____________
(x-2)(x+1)

How do you simplify that? Do you look for common factors? Or is it something else?

Answer 1

[ x ( x - 1 ) + ( x -1 ) ( x + 2 ) ] / [ ( x - 2 ) ( x + 1 ) ] =

( x - 1 ) [ x + ( x + 2 ) ] / [ ( x - 2 ) ( x + 1 ) ] =

( x - 1 ) ( x + x + 2 ) / [ ( x - 2 ) ( x + 1 ) ] =

( x - 1 ) ( 2 x + 2 ) / [ ( x - 2 ) ( x + 1 ) ] =

( x - 1 ) ∙ 2 ( x + 1 ) / [ ( x - 2 ) ( x + 1 ) ] =

2 ( x - 1 ) / ( x - 2 )

Answer 2

Thank you!