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$1) frac{3a+12b}{6ab} = frac{3*(a+4b)}{3*2ab}= frac{a+4b}{2ab}$
$2) frac{a^{2} -6a}{3 a^{2} } = frac{a(a-6)}{3a*a} = frac{a-6}{3a}$
$3) frac{5 y^{2} }{8 xy^{2}-3 y^{2} } = frac{5* y^{2} }{ y^{2} *(8x-3)} = frac{5}{8x-3}$
$4) frac{2 a^{2} b}{4 a^{2} -6ab} = frac{2a*ab}{2a*(2a-3b)} = frac{ab}{2a-3b}$
$5) frac{xy-3x}{6y-18}= frac{x*(y-3)}{6*(y-3)}= frac{x}{6}$
$6) frac{ac-5c}{3a-15}= frac{c*(a-5)}{3*(a-5)} = frac{c}{3}$