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$\fraction{4}{v + 3} = -\fraction{5}{2 v + 6} + 3 $
Solve for v
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2\times 4=-5+2\left(v+3\right)\times 3
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.
8=-5+2\left(v+3\right)\times 3
Multiply 2 and 4 to get 8.
8=-5+6\left(v+3\right)
Multiply 2 and 3 to get 6.
8=-5+6v+18
Use the distributive property to multiply 6 by v+3.
8=13+6v
Add -5 and 18 to get 13.
13+6v=8
Swap sides so that all variable terms are on the left hand side.
6v=8-13
Subtract 13 from both sides.
6v=-5
Subtract 13 from 8 to get -5.
v=\frac{-5}{6}
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.