Solve 1/3v-1/v=v+2/2v^2

$$\frac { 1 } { 3 v } - \frac { 1 } { v } = \frac { v + 2 } { 2 v ^ { 2 } }$$

Solve for v

$$v=-\frac{6}{7}\approx -0.857142857$$

Steps for Solving Linear Equation

Variable v cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 6v^{2}, the least common multiple of 3v,v,2v^{2}.

$$2v-6v=3\left(v+2\right)$$

Combine 2v and -6v to get -4v.

$$-4v=3\left(v+2\right)$$

Use the distributive property to multiply 3 by v+2.

$$-4v=3v+6$$

Subtract 3v from both sides.

$$-4v-3v=6$$

Combine -4v and -3v to get -7v.

$$-7v=6$$

Divide both sides by -7.

$$v=\frac{6}{-7}$$

Fraction \frac{6}{-7} can be rewritten as -\frac{6}{7} by extracting the negative sign.

$$v=-\frac{6}{7}$$