# x xx ( x + -3/x = 2)# is the first step which gives
# x^2 -3 = 2x # Now subtract #2x# from each side.
# x^2 - 2x -3 = 2x - 2x # resulting in
# x^2 - 2x - 3 = 0 # break this into two binomials.
#-3# means that one of the factors of three must be negative and one must be positive.
#-2# means that the negative factor must be larger than the positive factor.
The possible factors of #-3# are #1 x (-3)# and #-1 x (+3)# using the information above the correct choice is #+1 x -3# so
# ( x +1 ) xx ( x-3) = 0 # solve for each binomial
# x + 1 = 0 # subtract -1 from each side
# x + 1 -1 = 0 -1# so
#x = -1#
# x - 3 = 0 # add three to each side
# x -3 + 3 = 0 + 3 #
#x = + 3#
Put in this values to make sure there are no extraneous variables:
#-1+(-3/-1)=2#
That works. Now try the other one,
#3+(-3/3)=2#
That works too. So both work!
