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$-\fraction{3}{1 + 2} = -\fraction{6}{2 v - 4} + 1 $
Solve for v
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-\left(\frac{2}{3}v-\frac{4}{3}\right)\times 3=-6+2\left(v-2\right)
Variable v cannot be equal to 2 since division by zero is not defined. Multiply both sides of the equation by 2\left(v-2\right).
-\left(2v-4\right)=-6+2\left(v-2\right)
Use the distributive property to multiply \frac{2}{3}v-\frac{4}{3} by 3.
-2v+4=-6+2\left(v-2\right)
To find the opposite of 2v-4, find the opposite of each term.
-2v+4=-6+2v-4
Use the distributive property to multiply 2 by v-2.
-2v+4=-10+2v
Subtract 4 from -6 to get -10.
-2v+4-2v=-10
Subtract 2v from both sides.
-4v+4=-10
Combine -2v and -2v to get -4v.
-4v=-10-4
Subtract 4 from both sides.
-4v=-14
Subtract 4 from -10 to get -14.
v=\frac{-14}{-4}
Divide both sides by -4.
v=\frac{7}{2}
Reduce the fraction \frac{-14}{-4} to lowest terms by extracting and canceling out -2.