Question

Представьте в виде дроби 1/(xy-x^2)-1/(y^2-xy) в ответе 1/xy выражение 1/(a-3)^2 - 2/a^2-9 +1/(a+3)^2 в ответе 36/а^4-18а^2+81

Answer 1

$\displaystyle \frac{1}{xy-x^{2} }- \frac{1}{y^{2}-xy}= \frac{1}{x(y-x)}- \frac{1}{y(y-x)}= \frac{y-x}{xy(y-x)}= \frac{1}{xy}$

$\displaystyle \frac{1}{(a-3)^{2} }- \frac{2}{a^{2}-9}+ \frac{1}{(a+3)^{2}}= \frac{(a+3)^{2}-2(a-3)(a+3)+(a-3)^{2} }{(a-3)^{2}(a+3)^{2}}=\\\\\frac{a^{2}+6a+9-2a^{2}+18+a^{2}-6a+9 }{(a-3)^{2}(a+3)^{2}}= \frac{36}{(a^{2}-6a+9)(a^{2}+6a+9)}=\\\\=\frac{36}{a^{4}-a^{3}+9a^{2}+6a^{3}-36a^{2}+54a+9a^{2}-54a+81}=\frac{36}{a^{4}-18a^{2}+81}$