Equation is:
(2x – 5)/3 – 2 = (3x + 2)/5
What I would do first is get all the fractions on to one side.
Add 2 to both sides, then subtract the fraction on the right from both sides.
(2x – 5)/3 – (3x + 2)/5 = 2
Now look for a common denominator on the left. It's 15, so change both the fractions.
In the first we multiply top and bottom by 5 and in the second we multiply top and bottom by 3.
5(2x – 5)/15 – 3(3x + 2)/15 = 2
Because the denominators are the same we can combine the fractions.
[5(2x – 5) – 3(3x + 2)]/15 = 2
Now multiply both sides by 15.
[5(2x – 5) – 3(3x + 2)] = 30
We should be right from there.
[5(2x – 5) – 3(3x + 2)] = 30
10x – 25 – 9x – 6 = 30
x – 31 = 30
x = 61