Solve 4/v+3=-5/2v+6+3

$$\frac { 4 } { v + 3 } = - \frac { 5 } { 2 v + 6 } + 3$$

Solve for v

$$v=-\frac{5}{6}\approx -0.833333333$$

Steps for Solving Linear Equation

Variable v cannot be equal to -3 since division by zero is not defined. Multiply both sides of the equation by 2\left(v+3\right), the least common multiple of v+3,2v+6.

$$2\times 4=-5+2\left(v+3\right)\times 3$$

Multiply 2 and 4 to get 8.

$$8=-5+2\left(v+3\right)\times 3$$

Multiply 2 and 3 to get 6.

$$8=-5+6\left(v+3\right)$$

Use the distributive property to multiply 6 by v+3.

$$8=-5+6v+18$$

Add -5 and 18 to get 13.

$$8=13+6v$$

Swap sides so that all variable terms are on the left hand side.

$$13+6v=8$$

Subtract 13 from both sides.

$$6v=8-13$$

Subtract 13 from 8 to get -5.

$$6v=-5$$

Divide both sides by 6.

$$v=\frac{-5}{6}$$

Fraction \frac{-5}{6} can be rewritten as -\frac{5}{6} by extracting the negative sign.

$$v=-\frac{5}{6}$$