How do you simplify #(p^3-1)/(5-10p+5p^2)#?

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Answer 1 · 2017-01-24T13:08:48

#(p^3-1)/(5-10p+5p^2)=(p^2+p+1)/(5(p-1))# or #(p^2+p+1)/(5p-5)#

To simplify #(p^3-1)/(5-10p+5p^2)#, we should first factorize numerator and denomiantor.

#p^3-1=p^3-p^2+p^2-p+p-1#

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

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

and #5-10+5p^2=5(p^2-2p+1)#

= #5(p^2-p-p+1)=5(p(p-1)-1(p-1))=5(p-1)(p-1)#

Hence #(p^3-1)/(5-10p+5p^2)#

= #((p^2+p+1)(p-1))/(5(p-1)(p-1))#

= #((p^2+p+1)cancel((p-1)))/(5(p-1)cancel((p-1)))#

= #(p^2+p+1)/(5(p-1))# or #(p^2+p+1)/(5p-5)#