Solve v-2/v+10=v-3/v+3

$$\frac { v - 2 } { v + 10 } = \frac { v - 3 } { v + 3 }$$

Solve for v

$$v=4$$

Steps for Solving Linear Equation

Variable v cannot be equal to any of the values -10,-3 since division by zero is not defined. Multiply both sides of the equation by \left(v+3\right)\left(v+10\right), the least common multiple of v+10,v+3.

$$\left(v+3\right)\left(v-2\right)=\left(v+10\right)\left(v-3\right)$$

Use the distributive property to multiply v+3 by v-2 and combine like terms.

$$v^{2}+v-6=\left(v+10\right)\left(v-3\right)$$

Use the distributive property to multiply v+10 by v-3 and combine like terms.

$$v^{2}+v-6=v^{2}+7v-30$$

Subtract v^{2} from both sides.

$$v^{2}+v-6-v^{2}=7v-30$$

Combine v^{2} and -v^{2} to get 0.

$$v-6=7v-30$$

Subtract 7v from both sides.

$$v-6-7v=-30$$

Combine v and -7v to get -6v.

$$-6v-6=-30$$

Add 6 to both sides.

$$-6v=-30+6$$

Add -30 and 6 to get -24.

$$-6v=-24$$

Divide both sides by -6.

$$v=\frac{-24}{-6}$$

Divide -24 by -6 to get 4.

$$v=4$$