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factor out a term to cancel in a fraction


Hello group.

I'm trying to do a little algebra which i can do in my head using
Mathematica.  Why? Well, it's neater.

Consider the following.


p'[t] == (e0 s[t] k1 k2 )/ (s[t] k1 + k1 Km)

Factor out k1 and cancel it to simplify the expression. Why is this so
difficult to accomplish in mathematica?  Following does nothing.

p'[t] == (e0 s[t] k1 k2 )/ (s[t] k1 + k1 Km) //
 Assuming[k1 > 0, {Collect[#, k1]}] &


Thanks for any info.

Sean



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