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

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

Solve for v

$$v = -\frac{7}{2} = -3\frac{1}{2} = -3.5$$

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 -21.

$$6v=-21$$

Divide both sides by 6.

$$v=\frac{-21}{6}$$

Reduce the fraction \frac{-21}{6} to lowest terms by extracting and canceling out 3.

$$v=-\frac{7}{2}$$