\(a,\dfrac{3x^2y+4xy^2}{6x+8y}=\dfrac{xy\left(3x+4y\right)}{2\left(3x+4y\right)}=\dfrac{xy}{2}\\ b,\dfrac{-3x^2-6x}{4-x^2}=\dfrac{-3x\left(x-2\right)}{-\left(x-2\right)\left(x+2\right)}=\dfrac{x}{x+2}\\ c,\dfrac{8x^2y^2\left(x+y\right)}{4xy\left(x^2-y^2\right)}=\dfrac{4xy.\left(x+y\right).2xy}{4xy\left(x+y\right)\left(x-y\right)}=\dfrac{2xy}{x-y}\)
\(d,\dfrac{9x^3-18x}{3.\left(x^4-4\right)}=\dfrac{9x\left(x^2-2\right)}{3.\left(x^2-2\right)\left(x^2+2\right)}=\dfrac{9x}{3\left(x^2+2\right)}=\dfrac{3x}{x^2+2}\\ e,\dfrac{x\left(x+3\right)}{x^2\left(3+x\right)}=\dfrac{1}{x}\\ f,\dfrac{x^2-2x+1}{x^2-3x+2}=\dfrac{\left(x-1\right)\left(x-1\right)}{\left(x-1\right)\left(x-2\right)}=\dfrac{x-1}{x-2}\)
