Solve 8/9=v-8/v+9

$$\frac { 8 } { 9 } = \frac { v - 8 } { v + 9 }$$

Solve for v

$$v=144$$

Steps for Solving Linear Equation

Variable v cannot be equal to -9 since division by zero is not defined. Multiply both sides of the equation by 9\left(v+9\right), the least common multiple of 9,v+9.

$$8\left(v+9\right)=9\left(v-8\right)$$

Use the distributive property to multiply 8 by v+9.

$$8v+72=9\left(v-8\right)$$

Use the distributive property to multiply 9 by v-8.

$$8v+72=9v-72$$

Subtract 9v from both sides.

$$8v+72-9v=-72$$

Combine 8v and -9v to get -v.

$$-v+72=-72$$

Subtract 72 from both sides.

$$-v=-72-72$$

Subtract 72 from -72 to get -144.

$$-v=-144$$

Multiply both sides by -1.

$$v=144$$