Answer
$\dfrac{4m}{3m^{2}+7m-6}-\dfrac{m}{3m^{2}-14m+8}=\dfrac{m(3m-19)}{(3m-2)(m+3)(m-4)}$
Work Step by Step
$\dfrac{4m}{3m^{2}+7m-6}-\dfrac{m}{3m^{2}-14m+8}$
Factor the denominators of both rational expressions:
$\dfrac{4m}{3m^{2}+7m-6}-\dfrac{m}{3m^{2}-14m+8}=...$
$...=\dfrac{4m}{(m+3)(3m-2)}-\dfrac{m}{(3m-2)(m-4)}=...$
Evaluate the subtraction of the two rational expressions using the LCD, which is $(3m-2)(m+3)(m-4)$ in this case:
$...=\dfrac{4m(m-4)-m(m+3)}{(3m-2)(m+3)(m-4)}=...$
Simplify:
$...=\dfrac{4m^{2}-16m-m^{2}-3m}{(3m-2)(m+3)(m-4)}=...$
$...=\dfrac{3m^{2}-19m}{(3m-2)(m+3)(m-4)}=\dfrac{m(3m-19)}{(3m-2)(m+3)(m-4)}$
