What would be the solution for x in the rational equation:

x^2/(x-3)= (x+2)/(2x-5)


 ---- Cross-multiplying

 <===== As the polynomial's LARGEST exponent is 3, there will be 3 solutions!!

Using the RATIONAL ROOT THEOREM, we find that 2 is a solution/zero of the above trinomial, so x = 2, or x - 2 = 0.
Hence, x - 2 is a factor of the polynomial.

Using SYNTHETIC DIVISION, or LONG DIVISION of POLYNOMIALS, the other factor of the polynomial is the quadratic, , so the factors of  are: .
As  CANNOT be factored with INTEGERS, its solutions/zeroes can be found, either by COMPLETING the SQUARE
or using the QUADRATIC EQUATION formula. Using the latter, we get: 

 <==== QUADRATIC EQUATION formula, where: 


                           

                            

The 3 solutions/zeroes (1 RATIONAL and 2 IRRATIONAL):   ;    ;