\[\boxed{\text{58\ (58).\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
Пояснение.
Решение.
\[\textbf{а)}\ \frac{(a + b)^{2}}{\text{ab}} - \frac{(a - b)^{2}}{\text{ab}} = 4\]
\[\frac{a^{2} + 2ab + b^{2}}{\text{ab}} - \frac{a^{2} - 2ab + b^{2}}{\text{ab}} =\]
\[= 4\]
\[\frac{a^{2} + 2ab + b^{2} - a^{2} + 2ab - b^{2}}{\text{ab}} =\]
\[= 4\]
\[\frac{4\text{ab}}{\text{ab}} = 4\]
\[4 = 4\]
\[Что\ и\ требовалось\ доказать.\ \]
\[\textbf{б)}\ \frac{(a + b)^{2}}{a^{2} + b^{2}} + \frac{(a - b)^{2}}{a^{2} + b^{2}} = 2\]
\[\frac{a^{2} + 2ab + b^{2}}{a^{2} + b^{2}} + \frac{a^{2} - 2ab + b^{2}}{a^{2} + b^{2}} =\]
\[= 2\]
\[\frac{a^{2} + 2ab + b^{2} + a^{2} - 2ab + b^{2}}{a^{2} + b^{2}} =\]
\[= 2\]
\[\frac{{2a}^{2} + {2b}^{2}}{a^{2} + b^{2}} = 2\]
\[2 = 2\]
\[Что\ и\ требовалось\ доказать.\]