Solve -2/v+8=4/v+2

$$\frac { - 2 } { v + 8 } = \frac { 4 } { v + 2 }$$

Solve for v

$$v=-6$$

Steps for Solving Linear Equation

Variable v cannot be equal to any of the values -8,-2 since division by zero is not defined. Multiply both sides of the equation by \left(v+2\right)\left(v+8\right), the least common multiple of v+8,v+2.

$$\left(v+2\right)\left(-2\right)=\left(v+8\right)\times 4$$

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

$$-2v-4=\left(v+8\right)\times 4$$

Use the distributive property to multiply v+8 by 4.

$$-2v-4=4v+32$$

Subtract 4v from both sides.

$$-2v-4-4v=32$$

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

$$-6v-4=32$$

Add 4 to both sides.

$$-6v=32+4$$

Add 32 and 4 to get 36.

$$-6v=36$$

Divide both sides by -6.

$$v=\frac{36}{-6}$$

Divide 36 by -6 to get -6.

$$v=-6$$