Answer: To solve this equation, we'll start by getting all the terms with x on one side and all the constant terms on the other side. To do this, we'll subtract the 1/x terms from both sides:
2/3 + 1/x - 1/x = 2/5 - 3/x - 1/x
Simplifying the left side:
2/3 = 2/5 - 4/x
Adding 4/x to both sides:
2/3 + 4/x = 2/5
Multiplying both sides by the least common multiple of the denominators, which is 15:
10 + 60/x = 30/5
Expanding the right side:
10 + 60/x = 6
Subtracting 10 from both sides:
60/x = -4
Dividing both sides by 60:
1/x = -4/60
Dividing both sides by -1:
x = 15/4
So the solution to the equation is x = 15/4.
Explanation: