## Calculus with Applications (10th Edition)

The solution is $m=3$
$\dfrac{2m}{m-2}-\dfrac{6}{m}=\dfrac{12}{m^{2}-2m}$ Take out common factor $m$ from the denominator of the fraction on the right side of the equation: $\dfrac{2m}{m-2}-\dfrac{6}{m}=\dfrac{12}{m(m-2)}$ Multiply the whole equation by $m(m-2)$ $m(m-2)\Big[\dfrac{2m}{m-2}-\dfrac{6}{m}=\dfrac{12}{m(m-2)}\Big]$ $2m(m)-6(m-2)=12$ $2m^{2}-6m+12=12$ Eliminate $12$ from both sides: $2m^{2}-6m=0$ Take out common factor $2m$ from the left side: $2m(m-3)=0$ Set both factors equal to $0$ and solve each individual equation for $m$: $2m=0$ $m=\dfrac{0}{2}$ $m=0$ $m-3=0$ $m=3$ The original equation is undefined for $m=0$, so the solution is only $m=3$