[tex]The\ domain:\\v+10\neq0\ \wedge\ v+6\neq0\\v\neq-10\ \wedge\ v\neq-6\\\\\dfrac{4}{v+10}=\dfrac{6}{v+6}\ \ \ \ \ |\text{cross multiply}\\\\4(v+6)=6(v+10)\ \ \ \ |\text{use distributive property}\\\\(4)(v)+(4)(6)=(6)(v)+(6)(10)\\\\4v+24=6v+60\ \ \ \ \ |\text{subtract 24 from both sides}\\\\4v=6v+36\ \ \ \ |\text{subtract 6v from both sides}\\\\-2v=36\ \ \ \ |\text{divide both sides by (-2)}\\\\\boxed{v=-18}\in D[/tex]
