1/2v-4-1=-1/v-2

Solution for 1/2v-4-1=-1/v-2 equation:

1/2v-4-1=-1/v-2

We move all terms to the left:

1/2v-4-1-(-1/v-2)=0


Domain of the equation: 2v!=0

v!=0/2

v!=0

v∈R



Domain of the equation: v-2)!=0

v∈R


We add all the numbers together, and all the variables

1/2v-(-1/v-2)-5=0

We get rid of parentheses

1/2v+1/v+2-5=0

We calculate fractions


v/2v^2+2v/2v^2+2-5=0

We add all the numbers together, and all the variables

v/2v^2+2v/2v^2-3=0

We multiply all the terms by the denominator


v+2v-3*2v^2=0

We add all the numbers together, and all the variables

3v-3*2v^2=0

Wy multiply elements

-6v^2+3v=0

a = -6; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·(-6)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*-6}=\frac{-6}{-12}
=1/2
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*-6}=\frac{0}{-12}
=0
$