SOLUTION: Can you help me solve this equation? (x-2)/3-(x-3)/5=13/15

Question 106516: Can you help me solve this equation?
(x-2)/3-(x-3)/5=13/15
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
(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

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