2/2k-1=4/k

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

2/2k-1=4/k

We move all terms to the left:

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


Domain of the equation: 2k!=0

k!=0/2

k!=0

k∈R



Domain of the equation: k)!=0

k!=0/1

k!=0

k∈R


We add all the numbers together, and all the variables

2/2k-(+4/k)-1=0

We get rid of parentheses

2/2k-4/k-1=0

We calculate fractions


2k/2k^2+(-8k)/2k^2-1=0

We multiply all the terms by the denominator


2k+(-8k)-1*2k^2=0

Wy multiply elements

-2k^2+2k+(-8k)=0

We get rid of parentheses

-2k^2+2k-8k=0

We add all the numbers together, and all the variables

-2k^2-6k=0

a = -2; b = -6; c = 0;
Δ = b2-4ac
Δ = -62-4·(-2)·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6}{2*-2}=\frac{0}{-4}
=0
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6}{2*-2}=\frac{12}{-4}
=-3
$