Question

(3/(9-m^2 )+(2m-1)/(m-3)-(m^2-4)/(m^2+6m+9)×(m+3)/(m-2))÷m/(m-3)

Answer 1

$ttdisplaystyle (frac{3}{9-m^2} +frac{2m-1}{m-3}-frac{m^2-4}{m^2+6m+9}cdot frac{m+3}{m-2}): frac{m}{m-3}=\\ (frac{-3}{m^2-9}+frac{2m-1}{m-3}-frac{(m-2)(m+2)(m+3)}{(m+3)^2(m-2)})cdot frac{m-3}{m}=\\ (frac{-3+(2m-1)(m+3)}{(m-3)(m+3)}-frac{m+2}{m+3})cdot frac{m-3}{m}=\\ (frac{2m^2+6m-m-3-3-(m^2+2m-3m-6)}{(m+3)(m-3)})cdot frac{m-3}{m}=\\ frac{(m^2+6m)(m-3)}{(m+3)(m-3)m}=frac{m+6}{m+3}$