\(a,=\dfrac{3x-2-7x+4}{2xy}=\dfrac{-2\left(2x-1\right)}{2xy}=\dfrac{1-2x}{xy}\\ b,=\dfrac{3x+5-5+15x}{4x^3y}=\dfrac{18x}{4x^3y}=\dfrac{9}{2x^2y}\\ c,=\dfrac{4x+7-3x-6}{2x+2}=\dfrac{x+1}{2\left(x+1\right)}=\dfrac{1}{2}\\ d,=\dfrac{9x+5-5x+7}{2\left(x-1\right)\left(x+3\right)^2}=\dfrac{4\left(x+3\right)}{2\left(x-1\right)\left(x+3\right)^2}=\dfrac{2}{\left(x-1\right)\left(x+3\right)}\\ e,=\dfrac{xy+x^2}{\left(x-y\right)\left(x+y\right)}=\dfrac{x\left(x+y\right)}{\left(x-y\right)\left(x+y\right)}=\dfrac{x}{x-y}\)
\(f,=\dfrac{5xy+y^3-5xy+x^3}{x^2y^2}=\dfrac{x^3+y^3}{x^2y^2}\\ g,=\dfrac{2x^2-2x-x^2-x}{10\left(x+1\right)\left(x-1\right)}=\dfrac{x^2-3x}{10\left(x-1\right)\left(x+1\right)}\\ h,=\dfrac{x^2+9x-3x+9}{x\left(x-3\right)\left(x+3\right)}=\dfrac{\left(x+3\right)^2}{x\left(x-3\right)\left(x+3\right)}=\dfrac{x+3}{x\left(x-3\right)}\)
\(i,=\dfrac{3x-x+6}{2x\left(x+3\right)}=\dfrac{2\left(x+3\right)}{2x\left(x+3\right)}=\dfrac{1}{x}\\ j,=\dfrac{x^4-1-x^4+3x^2-2}{x^2-1}=\dfrac{3\left(x^2-1\right)}{x^2-1}=3\\ k,=\dfrac{x^2+4x+3+x^2-4x+3+2x-2x^2}{\left(x-3\right)\left(x+3\right)}=\dfrac{2\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}=\dfrac{2}{x-3}\\ l,=\dfrac{3x^2+4x+1-x^2+2x-1-x^2-2x+3}{\left(x-1\right)^2\left(x+1\right)}\\ =\dfrac{x^2+4x+3}{\left(x-1\right)^2\left(x+1\right)}=\dfrac{\left(x+1\right)\left(x+3\right)}{\left(x-1\right)^2\left(x+1\right)}=\dfrac{x+3}{\left(x-1\right)^2}\)
\(n,=\dfrac{5x-15+6x^3-8x-6x^3+54x}{2x\left(x+3\right)\left(x-3\right)}=\dfrac{51x-15}{2x\left(x-3\right)\left(x+3\right)}\\ m,=\dfrac{\left(3x+1\right)\left(x+1\right)^2-6\left(x^2-1\right)-\left(3x-2\right)\left(x-1\right)^2}{\left(x-1\right)^2\left(x+1\right)^2}\\ =\dfrac{9x^2-2x+9}{\left(x-1\right)^2\left(x+1\right)^2}\)
