a: \(\dfrac{10}{x+3}=\dfrac{60\left(x-3\right)}{6\left(x+3\right)\left(x-3\right)}\)
\(\dfrac{5}{2x-6}=\dfrac{15\left(x+3\right)}{6\left(x+3\right)\left(x-3\right)}\)
\(\dfrac{1}{9-3x}=\dfrac{-1}{3\left(x-3\right)}=\dfrac{-2\left(x+3\right)}{6\left(x+3\right)\left(x-3\right)}\)
b: \(\dfrac{7x^2-2x+5}{x^3-1}=\dfrac{7x^2-2x+5}{\left(x-1\right)\left(x^2+x+1\right)}\)
\(\dfrac{1-3x}{x^2+x+1}=\dfrac{\left(1-3x\right)\left(x-1\right)}{\left(x-1\right)\left(x^2+x+1\right)}\)
\(3=\dfrac{3\left(x^3-1\right)}{\left(x-1\right)\left(x^2+x+1\right)}\)
e: \(\dfrac{1}{x^3+1}=\dfrac{1}{\left(x+1\right)\left(x^2-x+1\right)}\)
\(\dfrac{2}{x+1}=\dfrac{2\left(x^2-x+1\right)}{\left(x+1\right)\left(x^2-x+1\right)}\)
\(\dfrac{3}{x^2-x+1}=\dfrac{3\left(x+1\right)}{\left(x+1\right)\left(x^2-x+1\right)}\)
