答案：解:(1)$\frac{y}{4x^{2}}=\frac{3y^{2}}{12x^{2}y}$,$\frac{5}{6xy}=\frac{10x}{12x^{2}y}$.
(2)$\frac{1}{4x^{3}y}=\frac{3y}{12x^{3}y^{2}}$,$\frac{4}{6xy^{2}}=\frac{8x^{2}}{12x^{3}y^{2}}$.
(3)$\frac{a}{2a+6}=\frac{a(a-3)}{2(a+3)(a-3)}$,$\frac{a-1}{a^{2}-9}=\frac{2a-2}{2(a+3)(a-3)}$.
(4)$\frac{2a}{a^{2}-9}=\frac{2a(a-3)}{(a-3)^{2}(a+3)}$,$\frac{3}{a^{2}-6a+9}=\frac{3(a+3)}{(a-3)^{2}(a+3)}$.
(5)$\frac{a-1}{(a+1)^{2}-4}=\frac{a-1}{(a+3)(a-1)}=\frac{1}{a+3}=\frac{2(a-1)}{2(a-1)(a+3)}$,
$\frac{1-a}{2-4a+2a^{2}}=\frac{1-a}{2(a-1)^{2}}=-\frac{1}{2(a-1)}=-\frac{a+3}{2(a-1)(a+3)}$.
(6)$\frac{1}{x^{2}-x}=\frac{x-1}{x(x-1)^{2}}$,$\frac{1}{x^{2}-2x+1}=\frac{x}{x(x-1)^{2}}$.
(7)$\frac{2x}{x^{2}-9}=\frac{4x}{2(x+3)(x-3)}$,$\frac{x}{2x+6}=\frac{x(x-3)}{2(x+3)(x-3)}$.
(8)$\frac{x}{4a(x+2)}=\frac{3bx}{12ab(x+2)}$,$\frac{y}{6b(x+2)}=\frac{2ay}{12ab(x+2)}$.
(9)$\frac{y}{2x}=\frac{6y^{3}}{12xy^{2}}$,$\frac{x}{3y^{2}}=\frac{4x^{2}}{12xy^{2}}$,$\frac{1}{4xy}=\frac{3y}{12xy^{2}}$.
(10)$\frac{x}{x-y}=\frac{x(x+y)^{2}}{(x+y)^{2}(x-y)}$,
$\frac{y}{x^{2}+2xy+y^{2}}=\frac{y(x-y)}{(x+y)^{2}(x-y)}$,
$\frac{2}{x^{2}-y^{2}}=\frac{2(x+y)}{(x+y)^{2}(x-y)}$.