Question 106516
(x-2)/3-(x-3)/5=13/15 

First, we will get rid of the fractions by multiplying each term by the Lowest Common Multiple (LCM)(the smallest number that 3,5 and 15 divides evenly into)------------By inspection, we see that this number is 15.

15*(x-2)/3-15*(x-3)/5=15*13/15 simplifying we get:

5(x-2)-3(x-3)=13  get rid of parens (distributive law)
5x-10-3x+9=13  simplify

2x-1=13  add 1 to both sides

2x-1+1=13+1  collect like terms

2x=14  divide both sides by 2

x=7

CK
(x-2)/3-(x-3)/5=13/15 
(7-2)/3-(7-3)/5=13/15 
5/3-4/5=13/15 
5/3=25/15 and 4/5=12/15, so:
25/15-12/15=13/15
13/15=13/15



Hope this helps---ptaylor