Simplifying a expression using factorization

Question

can anyone explain me how can I solved this problem ?

"Use factorization to simplify this expression:"

$\ \left( 6\over m+3 \right)^{-1} \left( 6 m^{2}-15 m-9 \over 2m^{2} -18 \right)^{-1} $

Thanks a lot.

Answer 1

hint:$$\ \left( 6\over m+3 \right)^{-1} \left( 6 m^{2}-15 m-9 \over 2m^{2} -18 \right)^{-1}=\\ \left( m+3\over 6 \right) \left( 2m^2-18\over 6 m^{2}-15 m-9\right)=\\ \ \left( m+3\over 6 \right) \left( 2(m^2-9)\over 3(2 m^{2}-5 m-3)\right)=\\ \left( m+3\over 6 \right) \left( 2(m^2-9)\over 3(2 m^{2}-5 m-3)\right)=\\\frac{2}{6\times 3}(m+3) \left( (m^2-9)\over (2 m^{2}-5 m-3)\right)=\\ \frac{1}{3\times 3}(m+3) \left( (m-3)(m+3)\over (2m+1)(m-3)\right)=\\ \frac{1}{3\times 3}(m+3) \left( \not{(m-3)}(m+3)\over (2m+1)\not(m-3)\right)=\\$$