-2/x-4=-4/1-x

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

-2/x-4=-4/1-x

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



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

We move all terms containing x to the left, all other terms to the right

-x)!=-1

x!=-1/1

x!=-1

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


1x*x+4*x-4*x-2=0

We add all the numbers together, and all the variables

1x*x-2=0

Wy multiply elements

x^2-2=0

a = 1; b = 0; c = -2;
Δ = b2-4ac
Δ = 02-4·1·(-2)
Δ = 8
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{8}=\sqrt{4*2}=\sqrt{4}*\sqrt{2}=2\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{2}}{2*1}=\frac{0-2\sqrt{2}}{2}
=-\frac{2\sqrt{2}}{2}
=-\sqrt{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{2}}{2*1}=\frac{0+2\sqrt{2}}{2}
=\frac{2\sqrt{2}}{2}
=\sqrt{2}
$