1/2k+4/k=k/k+2

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

1/2k+4/k=k/k+2

We move all terms to the left:

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


Domain of the equation: 2k!=0

k!=0/2

k!=0

k∈R



Domain of the equation: k!=0

k∈R



Domain of the equation: k+2)!=0

k∈R


We get rid of parentheses

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

Fractions to decimals

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

We calculate fractions


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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

9k-1*2k^2=0

Wy multiply elements

-2k^2+9k=0

a = -2; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·(-2)·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*-2}=\frac{-18}{-4}
=4+1/2
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*-2}=\frac{0}{-4}
=0
$