Solve 1/v+3v+12/v^2-5v=7v-30/v^2-5v

$$\frac { 1 } { v } + \frac { 3 v + 12 } { v ^ { 2 } - 5 v } = \frac { 7 v - 30 } { v ^ { 2 } - 5 v }$$

Solve for v

$$v = \frac{37}{3} = 12\frac{1}{3} \approx 12.333333333$$

Steps for Solving Linear Equation

Variable v cannot be equal to any of the values 0,5 since division by zero is not defined. Multiply both sides of the equation by v\left(v-5\right), the least common multiple of v,v^{2}-5v.

$$v-5+3v+12=7v-30$$

Combine v and 3v to get 4v.

$$4v-5+12=7v-30$$

Add -5 and 12 to get 7.

$$4v+7=7v-30$$

Subtract 7v from both sides.

$$4v+7-7v=-30$$

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

$$-3v+7=-30$$

Subtract 7 from both sides.

$$-3v=-30-7$$

Subtract 7 from -30 to get -37.

$$-3v=-37$$

Divide both sides by -3.

$$v=\frac{-37}{-3}$$

Fraction \frac{-37}{-3} can be simplified to \frac{37}{3} by removing the negative sign from both the numerator and the denominator.

$$v=\frac{37}{3}$$