Solve 8/v-1=-4/v-7

$$\frac { 8 } { v - 1 } = \frac { - 4 } { v - 7 }$$

Solve for v

$$v=5$$

Steps for Solving Linear Equation

Variable v cannot be equal to any of the values 1,7 since division by zero is not defined. Multiply both sides of the equation by \left(v-7\right)\left(v-1\right), the least common multiple of v-1,v-7.

$$\left(v-7\right)\times 8=\left(v-1\right)\left(-4\right)$$

Use the distributive property to multiply v-7 by 8.

$$8v-56=\left(v-1\right)\left(-4\right)$$

Use the distributive property to multiply v-1 by -4.

$$8v-56=-4v+4$$

Add 4v to both sides.

$$8v-56+4v=4$$

Combine 8v and 4v to get 12v.

$$12v-56=4$$

Add 56 to both sides.

$$12v=4+56$$

Add 4 and 56 to get 60.

$$12v=60$$

Divide both sides by 12.

$$v=\frac{60}{12}$$

Divide 60 by 12 to get 5.

$$v=5$$