Question

Remember to check for extraneous solutions

2/v + 2/3 = v-6/3v

A) {-12}
B) {4}
C) {2}
D) {-2}

Answer 1

The answer is A, sweetie

Answer 2

`Domain:v\\eq0\\\\(2)/(v)+(2)/(3)=(v-6)/(3v)\\\\(2\cdot3)/(v\cdot3)+(2\cdot v)/(3\cdot v)=(v-6)/(3v)\\\\(6)/(3v)+(2v)/(3v)=(v-6)/(3v)\\\\(6+2v)/(3v)=(v-6)/(3v)\iff6+2v=v-6\qquad\text{subtract 6 from both sides}\\\\2v=v-12\qquad\text{subtract v from both sides}\\\\\boxed{v=-12}\to\boxed{A.}`