How do you solve #x+ \frac { - 3} { x } = 2#?

1 Answer

Answer:

#x = -1 or 3#

Explanation:

# 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!