Найдите значение выражения a2−25b25ab:(15b−1a)\dfrac{a^2-25b^2}{5ab}:\left(\dfrac1{5b}-\dfrac1a \right)5aba2−25b2:(5b1−a1) при a=41419,b=2119a=4\frac{14}{19}, b=2\frac1{19}a=41914,b=2191▸Ответ15▸Решениеa2−25b25ab:(15b−1a)=\dfrac{a^2-25b^2}{5ab}:\left(\dfrac1{5b}-\dfrac1a \right)=5aba2−25b2:(5b1−a1)=(a−5b)(a+5b)5ab:a−5b5ab=\dfrac{(a-5b)(a+5b)}{5ab}:\dfrac{a-5b}{5ab}=5ab(a−5b)(a+5b):5aba−5b=(a−5b)(a+5b)5ab⋅5aba−5b=\dfrac{(a-5b)(a+5b)}{5ab} \cdot \dfrac{5ab}{a-5b}=5ab(a−5b)(a+5b)⋅a−5b5ab=a+5ba+5ba+5b Подставляем: 41419+5⋅2119=41419+10519=4\frac{14}{19} +5\cdot 2\frac1{19}=4\frac{14}{19} +10\frac5{19}=41914+5⋅2191=41914+10195=151515