MHB How to Solve a Differential Equation Using Separation of Variables?

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Can someone please help me solve the following using separation of variables:

dy/dx = (xy + 3x -y-3)/(xy -4x+6y-24)

so that the solution is written in the form: ((x+6)/(y+3))^7 =
 
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What do you get when you factor the numerator and denominator of the right side?
 

Thread 'A question about variables of integration'

I have the equation ##F^x=m\frac {d}{dt}(\gamma v^x)##, where ##\gamma## is the Lorentz factor, and ##x## is a superscript, not an exponent. In my textbook the solution is given as ##\frac {F^x}{m}t=\frac {v^x}{\sqrt {1-v^{x^2}/c^2}}##. What bothers me is, when I separate the variables I get ##\frac {F^x}{m}dt=d(\gamma v^x)##. Can I simply consider ##d(\gamma v^x)## the variable of integration without any further considerations? Can I simply make the substitution ##\gamma v^x = u## and then...
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