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 $(p^2+p+1)/(5p-5)$

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