still working this problem

[Lucy]

I have this much of the problem solved but I don't know wher to go from here to solve for x

4/2x+3 + 17/5x-3 =3

4(5x-3)/(2x+3)(5x-3) + 17(2x+3)/(5x-3)(2x+3) =3

20x -12 +34x+41/(2x+3)(5x-3) =3

54x+29/10x^2-9 =3

I don't know if I have done this correct, and where do I go from here?

 

[Gene]

First you need to buy a lot more ()s. I understand Wall-mart has a sale. You mean
4/(2x+3) + 17/(5x-3) =3
What you wrote is
(4/2)*x+ 3 + (17/5)*x - 3 = 3

You are all right up to
20x -12 +34x+41/(2x+3)(5x-3) =3
which should be
(20x -12 +34x+51)/((2x+3)(5x-3)) = 3
The next step is to get rid of the denominator.
(20x -12 +34x+51) = 3*(2x+3)(5x-3)
54x+39=30x²+27x-27
30x²-27x-66 = 0
10x²-9x-22 = 0
Not a nice quadratic but either the quadratic formula or some other trick will give
(10x+11)(x-2) = 0