Question

помогите плиз скоро надо сдавать..
Докажите тождество ​

Answer 1

$\displaystyle\bf\\1)\\\\\frac{a}{ab+b^{2} } +\frac{b}{a^{2}+ab } =\frac{a}{b\cdot(a+b) } +\frac{b}{a\cdot(a+b )} =\\\\\\=\frac{a\cdot a+b\cdot b}{ab(a+b)} =\frac{a^{2} +b^{2} }{ab(a+b)} \\\\2)\\\\\frac{a^{2} b}{a^{2} + b^{2} } \cdot\frac{a^{2} +b^{2} }{ab(a+b)} =\frac{a}{a+b} \\\\3)\\\\\frac{a^{2} }{a^{2} -b^{2} } -\frac{a}{a+b} =\frac{a^{2} }{(a -b)(a+b)} -\frac{a}{a+b} =\\\\\\=\frac{a^{2} -a\cdot(a-b)}{(a-b)(a+b)} =\frac{a^{2} -a^{2} +ab}{(a-b)(a+b)}=\frac{ab}{a^{2} -b^{2} }$

$\displaystyle\bf\\\frac{ab}{a^{2} -b^{2} } =\frac{ab}{a^{2} -b^{2} }$

Тождество доказано