Question

Упростите выражение под номером 5

Answer 1

$(frac{b^{1,5}+2}{b^{2,5}-2b^2}-frac{b^{1,5}-2}{b^{2,5}+2b^2})*frac{b-4}{b^{1,5}}=\\=frac{(b^{1,5}+2)*(b^{2,5}+2b^2)-(b^{1,5}-2)*(b^{2,5}-2b^2)}{(b^{2,5}-2b^2)*(b^{2,5}+2b^2)}*frac{b-4}{b^{1,5}}=\\=frac{b^{4}+2b^{2,5}+2b^{3,5}+4b^2)-(b^{4}-2b^{2,5}-2b^{3,5}+4b^2)}{(b^{2,5}-2b^2)*(b^{2,5}+2b^2)}*frac{b-4}{b^{1,5}}=\\=frac{b^{4}+2b^{2,5}+2b^{3,5}+4b^2-b^{4}+2b^{2,5}+2b^{3,5}-4b^2}{(b^{2,5}-2b^2)*(b^{2,5}+2b^2)}*frac{b-4}{b^{1,5}}=$

$=frac{4b^{2,5}+4b^{3,5}}{(b^{2,5}-2b^2)*(b^{2,5}+2b^2)}*frac{b-4}{b^{1,5}}=\\=frac{4b^{2,5}*(1+4b)}{(b^{2,5})^2-(2b^2)^2}*frac{b-4}{b^{1,5}}=\\=frac{4b^{2,5}*(1+4b)}{b^{5}-4b^4}*frac{b-4}{b^{1,5}}=\\=frac{4b^{2,5}*(1+4b)}{b^{4}*(b-4)}*frac{b-4}{b^{1,5}}=\\=frac{4b^{2,5-1,5}*(1+4b)}{b^{4}}=frac{4b*(1+4b)}{b^{4}}=frac{4(1+4b)}{b^{3}}$