Упражнение 101

\(1)\ {\frac{9-5b}{b}}^{\backslash{c}}-{\frac{7-5c}{c}}^{\backslash{b}}=\frac{ c(9-5b)-b(7-5c)}{bc}=\frac{9c-5bc-7b+5bc}{bc}=\frac{9c-7b}{bc};\)

\(2)\ {\frac{4d+7}{7d}}^{\backslash6}-{\frac{d-6}{6d}}^{\backslash7}=\frac{ 6(4d+7)-7(d-6)}{42d}=\frac{24d+42-7d+42}{42d}=\frac{17d+84}{42d};\)

\(3)\ {\frac{5-k}{5p}}^{\backslash{k}}-{\frac{p+10}{5k}}^{\backslash{p}}=\frac{ k(5-k)-p(p+10)}{5kp}=\frac{5k-k^2-p^2-10p}{5kp};\)

\(4)\ {\frac{m-n}{mn}}^{\backslash{p}}-{\frac{p-n}{np}}^{\backslash{m}}=\frac{ p(m-n)-m(p-n)}{mnp}=\frac{mp-np-mp+mn}{mnp}=\frac{mn-np}{mnp}=\frac{ n(m-p)}{mnp}=\frac{m-p}{mp};\)

\(5)\ {\frac{6a+2}{ab}}^{\backslash{a}}-{\frac{2a+4}{a^2b}}^{\backslash1}=\frac{ a(6a+2)-(2a+4)}{a^2b}=\frac{6a^2+2a-2a-4}{a^2b}=\frac{6a^2-4}{a^2b};\)

\(6)\ {\frac{c^2-16}{c^6}}^{\backslash1}-{\frac{c-9}{c^5}}^{\backslash{c}}=\frac{c^2-16-c(c-9)}{c^6}=\frac{c^2-16-c^2+9c}{c^6}=\frac{9c-16}{c^6};\)

\(7)\ {\frac{1}{x^3}}^{\backslash{x^2}}-{\frac{1+x^2}{x^5}}^{\backslash1}=\frac{x^2-(1+x^2)}{x^5}=\frac{x^2-1-x^2}{x^5}=\frac{{-}1}{x^5}={-}\frac{1}{x^5};\)

\(8)\ {\frac{1-ab}{abc}}^{\backslash{d}}-{\frac{1-ad}{acd}}^{\backslash{b}}=\frac{ d(1-ab)-b(1-ad)}{abcd}=\frac{d-abd-b+abd}{abcd}=\frac{d-b}{abcd}.\)