Question

Найдите значение выражения

Answer 1

$\frac{2a}{4a^{2}-10ab} - \frac{5b}{4a^{2}-25b^{2}}= \frac{2a}{2a(2a-5b)} - \frac{5b}{(2a-5)(2a+5b)}= \\ = \frac{2a(2a+5b)-10ab}{2a(4a^{2}-25b^{2})} = \frac{4a^{2}+10ab-10ab}{2a(4a^{2}-25b^{2})}= \\ = \frac{4a^{2}}{2a(4a^{2}-25b^{2})} = \frac{2a}{(4a^{2}-25b^{2})}= \\ = \frac{10}{4*25 - 25*( \sqrt{3})^2 }= \frac{10}{100-75}= \frac{10}{25}= 0,4$