In the same way that you can always divide by #1#, you can also divide by #-1#.
The only difference is that dividing by #-1# makes the signs change,
Consider the following:
#3x+5y -2z = 1(3x+5y-2z)#
Compare with:
#3x+5y-2z = -1(-3x-5y+2z)#
If you multiply the factor of #-1# back into the bracket you will get the same expression you started with.
It is very useful when you need to change the signs.
For example to factorise the expression:
#3x(2a-b)" " color(blue)(+5y(b-2a)) - 7z(2a-b)" "larr# change signs
#=3x(2a-b) " "color(blue)(-5y(-b+2a)) - 7z(2a-b)#
#=3x(2a-b) " "color(blue)(-5y(2a-b)) - 7z(2a-b)#
There is now a common bracket:
#(2a-b)(3x-5y-7z)#
Or in simplifying a fraction:
#(color(red)((x-3y))(2x+5))/(color(red)((3y-x))(x-4))" "larr# brackets are different
#(color(red)(-(-x+3y))(2x+5))/(color(red)((3y-x))(x-4))#
#(color(red)(-cancel((3y-x)))(2x+5))/(color(red)(cancel((3y-x)))(x-4))#
#= -((2x+5))/((x-4))#
