a: \(\dfrac{5}{6xy^2}=\dfrac{5\cdot3\cdot x}{18x^2y^2}=\dfrac{15x}{18x^2y^2}=\dfrac{15x^2}{18x^3y^2}\)
\(\dfrac{2}{9x^3y}=\dfrac{2\cdot2y}{18x^3y^2}=\dfrac{4y}{18x^3y^2}\)
b: \(\dfrac{5}{14x^2y}=\dfrac{5\cdot y^4\cdot3}{42x^2y^5}=\dfrac{15y^4}{42x^2y^5}\)
\(\dfrac{4}{21xy^5}=\dfrac{4\cdot2\cdot x}{42x^2y^5}=\dfrac{8x}{42x^2y^5}\)
c: \(\dfrac{2x}{\left(x+2\right)^3}=\dfrac{4x^2}{2x\left(x+2\right)^3}\)
\(\dfrac{x-2}{2x\left(x+2\right)^2}=\dfrac{\left(x-2\right)\left(x+2\right)}{2x\left(x+2\right)^3}=\dfrac{x^2-4}{2x\left(x+2\right)^3}\)
d: \(\dfrac{7x-1}{2x^2+6x}=\dfrac{7x-1}{2x\left(x+3\right)}=\dfrac{\left(7x-1\right)\left(x-3\right)}{2x\left(x+3\right)\left(x-3\right)}\)
\(\dfrac{5-3x}{x^2-9}=\dfrac{2x\left(5-3x\right)}{2x\left(x-3\right)\left(x+3\right)}\)
f: \(\dfrac{x-1}{2x+2}=\dfrac{\left(x-1\right)^2}{2\left(x+1\right)\left(x-1\right)}\)
\(\dfrac{x+1}{2x-2}=\dfrac{\left(x+1\right)^2}{2\left(x-1\right)\left(x+1\right)}\)
\(\dfrac{1}{x^2-1}=\dfrac{2}{2\left(x-1\right)\left(x+1\right)}\)
