Solve v-1/8v+1/10=1/v

$$\frac { v - 1 } { 8 v } + \frac { 1 } { 10 } = \frac { 1 } { v }$$

Solve for v

$$v=5$$

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 40v, the least common multiple of 8v,10,v.

$$5\left(v-1\right)+40v\times \frac{1}{10}=40$$

Use the distributive property to multiply 5 by v-1.

$$5v-5+40v\times \frac{1}{10}=40$$

Multiply 40 and \frac{1}{10} to get 4.

$$5v-5+4v=40$$

Combine 5v and 4v to get 9v.

$$9v-5=40$$

Add 5 to both sides.

$$9v=40+5$$

Add 40 and 5 to get 45.

$$9v=45$$

Divide both sides by 9.

$$v=\frac{45}{9}$$

Divide 45 by 9 to get 5.

$$v=5$$