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Question Number 66855 by John Kaloki Musau last updated on 20/Aug/19

simplify  ((p^2 +2pq+q^2 )/(p^3 −pq^2 +p^2 q−q^3 ))

$${simplify} \\ $$$$\frac{{p}^{\mathrm{2}} +\mathrm{2}{pq}+{q}^{\mathrm{2}} }{{p}^{\mathrm{3}} −{pq}^{\mathrm{2}} +{p}^{\mathrm{2}} {q}−{q}^{\mathrm{3}} } \\ $$

Answered by $@ty@m123 last updated on 20/Aug/19

(((p+q)^2 )/(p^3 −q^3 +pq(p−q)))  (((p+q)^2 )/((p−q)(p^2 +pq+q^2 )+pq(p−q)))  (((p+q)^2 )/((p−q)(p^2 +pq+q^2 +pq)))  (((p+q)^2 )/((p−q)(p+q)^2 ))  (1/(p−q))

$$\frac{\left({p}+{q}\right)^{\mathrm{2}} }{{p}^{\mathrm{3}} −{q}^{\mathrm{3}} +{pq}\left({p}−{q}\right)} \\ $$$$\frac{\left({p}+{q}\right)^{\mathrm{2}} }{\left({p}−{q}\right)\left({p}^{\mathrm{2}} +{pq}+{q}^{\mathrm{2}} \right)+{pq}\left({p}−{q}\right)} \\ $$$$\frac{\left({p}+{q}\right)^{\mathrm{2}} }{\left({p}−{q}\right)\left({p}^{\mathrm{2}} +{pq}+{q}^{\mathrm{2}} +{pq}\right)} \\ $$$$\frac{\left({p}+{q}\right)^{\mathrm{2}} }{\left({p}−{q}\right)\left({p}+{q}\right)^{\mathrm{2}} } \\ $$$$\frac{\mathrm{1}}{{p}−{q}} \\ $$

Commented by John Kaloki Musau last updated on 20/Aug/19

wow! u got it.thanks

$${wow}!\:{u}\:{got}\:{it}.{thanks} \\ $$

Answered by Mr Jor last updated on 25/Aug/19

((p^2 +pq+pq+q^2 )/(p(p^2 −q^2 )+q(p^2 −q^2 )))  ((p(p+q)+q(p+q))/((p+q)(p^2 −q^2 )))  (((p+q)(p+q))/((p+q)(p−q)(p+q)))                =(1/(p−q))

$$\frac{\boldsymbol{{p}}^{\mathrm{2}} +\boldsymbol{{pq}}+\boldsymbol{{pq}}+\boldsymbol{{q}}^{\mathrm{2}} }{\boldsymbol{{p}}\left(\boldsymbol{{p}}^{\mathrm{2}} −\boldsymbol{{q}}^{\mathrm{2}} \right)+\boldsymbol{{q}}\left(\boldsymbol{{p}}^{\mathrm{2}} −\boldsymbol{{q}}^{\mathrm{2}} \right)} \\ $$$$\frac{\boldsymbol{{p}}\left(\boldsymbol{{p}}+\boldsymbol{{q}}\right)+\boldsymbol{{q}}\left(\boldsymbol{{p}}+\boldsymbol{{q}}\right)}{\left(\boldsymbol{{p}}+\boldsymbol{{q}}\right)\left(\boldsymbol{{p}}^{\mathrm{2}} −\boldsymbol{{q}}^{\mathrm{2}} \right)} \\ $$$$\frac{\left(\boldsymbol{{p}}+\boldsymbol{{q}}\right)\left(\boldsymbol{{p}}+\boldsymbol{{q}}\right)}{\left(\boldsymbol{{p}}+\boldsymbol{{q}}\right)\left(\boldsymbol{{p}}−\boldsymbol{{q}}\right)\left(\boldsymbol{{p}}+\boldsymbol{{q}}\right)} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\frac{\mathrm{1}}{\boldsymbol{{p}}−\boldsymbol{{q}}} \\ $$

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