((A^2 +ax +x^2)/ (a^3+ x^3)) *(( a^2 - ax+x^2)/(a^3-x^3 )). Created by mishenina98. matematika-ru

(a^3-x^3 ))...

zhenyaM2002

Verified answer

По формулам сокращенного умножения:
$\frac{a^2+ax+x^2}{a^3 +x^3} * \frac{a^2-ax+x^2}{a^3-x^3} = \\ \\ 
= \frac{a^2+ax+x^2}{(a +x)(a^2-ax+b^2)} * \frac{a^2-ax+x^2}{(a-x)(a^2+ax+x^2)} = \\ \\ 
= \frac{1}{(a+x)} * \frac{1}{(a-x)} = \frac{1}{a^2-x^2}$

2 votes Thanks 1

skvrttt $\frac{a^2+ax+x^2}{a^3+x^3}*\frac{a^2-ax+x^2}{a^3-x^3}=\frac{a^2+ax+x^2}{(a+x)(a^2-ax+x^2)}*\frac{a^2-ax+x^2}{(a-x)(a^2+ax+x^2)}=\\\frac{1}{a+x}*\frac{1}{a-x}=\frac{1}{(a+x)(a-x)}=(a^2-x^2)^{-1}$

2 votes Thanks 2

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