4x-3/3 - 6x-3/5 = 2

Question

I am not sure how to solve this.

Answer 1

As you wrote it, the problem is 4x - (3/3) - 6x - (3/5) = 2, which is solved as follows:

 

4x - 1 - 6x - 3/5 = 2                   [3/3 = 1]

 

-2x = 2 + 1 + 3/5                      [2 = 10/5, 1= 5/5]

 

-2x = 18/5

 

x = -9/5

 

However, what you probably intended to write is (4x-3)/3 - (6x-3)/5 = 2.  To solve this problem, first put the two rational expressions over a common denominator (15):

 

5*(4x-3)/3*5 - 3*(6x-3)/5*3 = 2

 

(20x-15-18x+9)/15 = 2

 

2x - 6 = 30

 

2x = 36

 

x = 18

 

Please use parentheses to make it clear what's in the numerator and denominator.