\(a,=\dfrac{6x+12+4-2x}{30}=\dfrac{4x+16}{30}=\dfrac{2x+4}{15}\\ b,=\dfrac{6x+8x-4+6-3x}{60}=\dfrac{11x+2}{60}\\ c,=\dfrac{x^2+2x+1-x^2-3}{2\left(x-1\right)\left(x+1\right)}=\dfrac{2\left(x-1\right)}{2\left(x-1\right)\left(x+1\right)}=\dfrac{1}{x+1}\\ d,=\dfrac{-4x^2+4x-1+4x^2-1}{2x\left(2x-1\right)}=\dfrac{2\left(2x-1\right)}{2x\left(2x-1\right)}=\dfrac{1}{x}\\ e,=\dfrac{x^2-2xy+y^2}{xy\left(x-y\right)}=\dfrac{\left(x-y\right)^2}{xy\left(x-y\right)}=\dfrac{x-y}{xy}\\ f,=\dfrac{1}{x-4}+\dfrac{2}{2-x}+\dfrac{1}{x+2}\\ =\dfrac{1}{x-4}+\dfrac{2x+4+2-x}{\left(x+2\right)\left(2-x\right)}=\dfrac{1}{x-4}+\dfrac{x+6}{\left(x+2\right)\left(2-x\right)}\\ =\dfrac{4-x^2+x^2+2x-24}{\left(x-4\right)\left(x+2\right)\left(2-x\right)}=\dfrac{2x-20}{\left(x-4\right)\left(x+2\right)\left(2-x\right)}\)
\(g,=\dfrac{2x-10xy+10xy-2x^2+2xy+4y^2}{2xy}=\dfrac{4y^2+2xy+2x-2x^2}{2xy}=\dfrac{2y^2+xy+x-x^2}{xy}\\ h,=\dfrac{2x-2y+x+y-3}{\left(x-y\right)\left(x+y\right)}=\dfrac{3x-y-3}{\left(x-y\right)\left(x+y\right)}\\ i,=\dfrac{2x}{x^2+2y}+\dfrac{1}{x-2y}+\dfrac{4}{x^2-4y^2}\\ =\dfrac{2x}{x^2+2y}+\dfrac{x+2y+4}{\left(x-2y\right)\left(x+2y\right)}=\dfrac{2x^3-8xy^2+\left(x^2+2y\right)\left(x+2y+4\right)}{\left(x^2+2y\right)\left(x+2y\right)\left(x-2y\right)}\)
\(k,=\dfrac{x^2+xy+y^2-3xy+x^2-2xy+y^2}{\left(x-y\right)\left(x^2+xy+y^2\right)}\\ =\dfrac{2\left(x-y\right)^2}{\left(x-y\right)\left(x^2+xy+y^2\right)}=\dfrac{2\left(x-y\right)}{x^2+xy+y^2}\\ l,=\dfrac{4x^2+4xy+y^2-16x^2+4x^2-4xy+y^2}{x\left(2x-y\right)\left(2x+y\right)}\\ =\dfrac{-8x^2+2y^2}{x\left(4x^2-y^2\right)}=\dfrac{-2\left(4x^2-y^2\right)}{x\left(4x^2-y^2\right)}=\dfrac{-2}{x}\)
