# How do you solve #x/3 - 2/3 = 1/x#?

##### 1 Answer

#### Answer:

#### Explanation:

First we want to eliminate all of the denominators. To do so, multiply everything by

#3x(x/3) - 3x(2/3) = 3x(1/x)#

#x^2 - 2x = 3#

Move the

#x^2 - 2x - 3 = 0#

This is factorable. We need numbers that add to

#(x+1)(x-3) = 0#

Ergo,

#-1/3 - 2/3 = 1/-1#

#-3/3 = 1/-1#

yes!

#3/3 - 2/3 = 1/3#

yes!