Question about a Question: Simplifying FractionsIn a question I asked several weeks ago an interim step reached was a.):1(x−6)!6!=1(x−4)!4!hence b.):(x−4)!(x−6)!=6!4!I'm not following how we got from a.) to b.)Help?

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Question about a Question: Simplifying FractionsIn a question I asked several weeks ago an interim step reached was a.):1(x−6)!6!=1(x−4)!4!hence b.):(x−4)!(x−6)!=6!4!I&#039;m not following how we got from a.) to b.)Help?

Korbin Ochoa · Accepted Answer

Cross multiply.Multiplying both sides by 6! you get1(x−6)!6!=1(x−4)!4!6!(x−6)!6!=6!(x−4)!4!Now the 6! factor in the numerator and denominator on the left hand side cancel, and you get1(x−6)!=6!(x−4)!4!.Now multiply both sides by (x−4)! to get(x−4)!(x−6)!=(x−4)!6!(x−4)!4!.Again, you have a factor of (x−4)! in both the numerator and denominator of the right hand side, so these cancel. You end up with(x−4)!(x−6)!=6!4!,as desired.P.S. It would have made more sense to follow-up that answer with a query in comments (and even more sense not to accept the answer until you understood all the steps!)

Korbin Rivera · Accepted Answer

Multiply both sides by (x−4)! and 6! and you will have (b)1(x−6)!6!=1(x−4)!4!⇔(x−4)!6!(x−6)!6!=(x−4)!6!(x−4)!4!as 6!6!=1 and (x−4)(x−4)=1, it simplifies to(x−4)!(x−6)!=6!4!

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