Question

solve for k. 9/2k-3=4/k+1

Answer 1

You'll need to use parentheses here to convey this problem accurately to possible helpers.  Unsure of whether you mean (9/2)k -3 or  9 / (2k-3).

I will assume that you mean:

    9           4
------- = ---------
2k-3        k+1

Cross mult:  9k+9=8k-12, so k= -21.

If that's not what you expected, then try again to present the problem without ambiguities.