4/2x+4=8/x-1

Solution for 4/2x+4=8/x-1 equation:

4/2x+4=8/x-1

We move all terms to the left:

4/2x+4-(8/x-1)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: x-1)!=0

x∈R


We get rid of parentheses

4/2x-8/x+1+4=0

We calculate fractions


4x/2x^2+(-16x)/2x^2+1+4=0

We add all the numbers together, and all the variables

4x/2x^2+(-16x)/2x^2+5=0

We multiply all the terms by the denominator


4x+(-16x)+5*2x^2=0

Wy multiply elements

10x^2+4x+(-16x)=0

We get rid of parentheses

10x^2+4x-16x=0

We add all the numbers together, and all the variables

10x^2-12x=0

a = 10; b = -12; c = 0;
Δ = b2-4ac
Δ = -122-4·10·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12}{2*10}=\frac{0}{20}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12}{2*10}=\frac{24}{20}
=1+1/5
$