How do you write this easier?

Question

#(1+(2+p)/p)/((p+1)^2-(p+1)^3)#

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Answer 1 · 2017-07-05T13:20:59

I got: #-2/(p^2(p+1))#

We can rearrange our expression by solving the numerator (common denominator) and collecting #(p+1)^2# in the denominator:

#((p+2+p)/p)/((p+1)^2[1-(p+1)])=((p+2p)/p)/((p+1)^2[cancel(1)-pcancel(-1)])=#

collect #p# and change the big fraction into a multiplication:

#=(2cancel((p+1)))/p*1/(-p(p+1)^cancel(2))=-2/(p^2(p+1))#

Answer 2 · 2017-07-05T13:31:45

#-2/(p^2(p+1))#

#((p+2+p)/p)/((p+1)^2(1-(p+1)))=(2(p+1))/(p((p+1)^2(1-(p+1))))=-2/(p^2(p+1))#