\(1)\ {\frac{a+7}{12}}^{\backslash3}+{\frac{a-4}{9}}^{\backslash4}=\frac{ 3(a+7)+4(a-4)}{36}=\frac{3a+21+4a-16}{36}=\frac{7a+5}{36};\)
\(2)\ {\frac{2b-7c}{6}}^{\backslash5}-{\frac{3b+2c}{15}}^{\backslash2}=\frac{ 5(2b-7c)-2(3b+2c)}{30}=\frac{10b-35c-6b-4c}{30}=\frac{4b-39c}{30};\)
\(3)\ {\frac{3x-2}{x}}^{\backslash{y}}-{\frac{3y-1}{y}}^{\backslash{x}}=\frac{ y(3x-2)-x(3y-1)}{xy}=\frac{3xy-2y-3xy+x}{xy}=\frac{x-2y}{xy};\)
\(4)\ {\frac{6p+1}{p}}^{\backslash3}-{\frac{2p+8}{3p}}^{\backslash1}=\frac{ 3(6p+1)-(2p+8)}{3p}=\frac{18p+3-2p-8}{3p}=\frac{16p-5}{3p};\)
\(5)\ {\frac{5m-n}{14m}}^{\backslash1}-{\frac{m-6n}{7m}}^{\backslash2}=\frac{5m-n-2(m-6n)}{14m}=\frac{5m-n-2m+12n}{14m}=\frac{3m+11n}{14m};\)
\(6)\ {\frac{x+4}{11x}}^{\backslash{y}}-{\frac{y-3}{11y}}^{\backslash{x}}=\frac{ y(x+4)-x(y-3)}{11xy}=\frac{xy+4y-xy+3x}{11xy}=\frac{4y+3x}{11xy};\)
\(7)\ {\frac{a+b}{ab}}^{\backslash{c}}+{\frac{a-c}{ac}}^{\backslash{b}}=\frac{ c(a+b)+b(a-c)}{abc}=\frac{ac+bc+ab-bc}{abc}=\frac{ac+ab}{abc}=\frac{ a(c+b)}{abc}=\frac{c+b}{bc};\)
\(8)\ {\frac{2}{p^2}}^{\backslash1}+{\frac{p-1}{p}}^{\backslash{p}}=\frac{2+p(p-1)}{p^2}=\frac{p^2-p+2}{p^2};\)
\(9)\ {\frac{k+4}{k}}^{\backslash{k}}-{\frac{3k-4}{k^2}}^{\backslash1}=\frac{ k(k+4)-(3k-4)}{k^2}=\frac{k^2+4k-3k+4}{k^2}=\frac{k^2+k+4}{k^2};\)
\(10)\ {\frac{x-y}{x^3}}^{\backslash{y}}-{\frac{y-x^2}{x^2y}}^{\backslash{x}}=\frac{ y(x-y)-x(y-x^2)}{x^3y}=\frac{xy-y^2-xy+x^3}{x^3y}=\frac{x^3-y^2}{x^3y};\)
\(11)\ {\frac{2m-3n}{m^2n}}^{\backslash{n}}+{\frac{7m-2n}{mn^2}}^{\backslash{m}}=\frac{ n(2m-3n)+m(7m-2n)}{m^2n^2}=\frac{2mn-3n^2+7m^2-2mn}{m^2n^2}=\frac{7m^2-3n^2}{m^2n^2};\)
\(12)\ {\frac{c+d}{cd^4}}^{\backslash{c^2}}-{\frac{c^2-8d}{c^3d^3}}^{\backslash{d}}=\frac{ c^2(c+d)-d(c^2-8d)}{c^3d^4}=\frac{c^3+c^2d-c^2d+8d^2}{c^3d^4}=\frac{c^3+8d^2}{c^3d^4}.\)
