Solve the equation (2X + 3) / (X-4) - (2X - 8) / (2X + 1) = 1

In order to solve this equation we need to find a common denominator for the 2 fractions. It is impossible to name the common denominator while working with unknown variables such as x,y etc. but we know from working with numbers that in order to find the common denominator of 2 or more fractions we need to find the common multiple of the denominators. In our case the common multiple is simply the product of our two denominators.  Which means ( X - 4 ) x  ( 2X + 1)  is our common denominator. And we need to multiple each fraction by the opposite's denominator. This results in our fraction looking like this     [ ( 2X + 3)( 2X + 1)  - ( 2X - 8)( X - 4) ] / ( X - 4 ) x  ( 2X + 1) 

After multiplying the paranthesis term by term we are left with     (4X² + 8X + 3  -  2X² + 8X + 8X - 32 ) /  ( X - 4 ) x  ( 2X + 1)   = 1 .  Having a fraction on one side and just a number on the other side means we can simply multiple the number the number with the denominator of the fraction and totally get rid of the denominator. This results in our equation looking like this 2X² + 24X - 29 = 2X² - 7X -4  moving everything to the left side of the equation and we get 31X -25 = 0 now we can move 25 to the right          31X = 25  and we simply solve for X. In the end X = 25/31  which is roughly 0.81