Solve 5/v-4-8/v+1=34/v^2-3v-4

$$\frac { 5 } { v - 4 } - \frac { 8 } { v + 1 } = \frac { 34 } { v ^ { 2 } - 3 v - 4 }$$

Solve for v

$$v=1$$

Steps for Solving Linear Equation

Variable v cannot be equal to any of the values -1,4 since division by zero is not defined. Multiply both sides of the equation by \left(v-4\right)\left(v+1\right), the least common multiple of v-4,v+1,v^{2}-3v-4.

$$\left(v+1\right)\times 5-\left(v-4\right)\times 8=34$$

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

$$5v+5-\left(v-4\right)\times 8=34$$

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

$$5v+5-\left(8v-32\right)=34$$

To find the opposite of 8v-32, find the opposite of each term.

$$5v+5-8v+32=34$$

Combine 5v and -8v to get -3v.

$$-3v+5+32=34$$

Add 5 and 32 to get 37.

$$-3v+37=34$$

Subtract 37 from both sides.

$$-3v=34-37$$

Subtract 37 from 34 to get -3.

$$-3v=-3$$

Divide both sides by -3.

$$v=\frac{-3}{-3}$$

Divide -3 by -3 to get 1.

$$v=1$$