Question

Упростите выражения (25b/a-100a/b)*1/5b+10a

Answer 1

$(\frac{25b}{a} - \frac{100a}{b} )* \frac{1}{5b} +10a= \\ 1) \frac{25 b^{2}-100 a^{2}}{ab} = \frac{25(b^{2}-4a^{2})}{ab} \\ 2) \frac{25(b^{2}-4a^{2})}{ab} * \frac{1}{5b} = \frac{25(b^{2}-4a^{2})} {5ab^{2}}= \frac{5(b^{2}-4a^{2})}{ab^{2}} \\ 3)\frac{5(b^{2}-4a^{2})}{ab^{2}} + \frac{10a}{1}= \frac{5(b^{2}-4a^{2})}{ab^{2}}+\frac{10a^{2}b^{2}}{ab^{2}}=$
$\frac{5(b^{2}-4a^{2})+10a^{2}b^{2}}{ab^{2}}= \frac{5b^{2}-20a^{2}+10a^{2}b^{2}}{ab} = \frac{5(b^{2}-4a^{2}+2a^{2}b^{2})}{ab}$