-4/x+1=5/1-x

Solution for -4/x+1=5/1-x equation:

-4/x+1=5/1-x

We move all terms to the left:

-4/x+1-(5/1-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

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

We get rid of parentheses

-4/x+1x+1=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

x+1x*x-4=0

Wy multiply elements

x^2+x-4=0

a = 1; b = 1; c = -4;
Δ = b2-4ac
Δ = 12-4·1·(-4)
Δ = 17
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{17}}{2*1}=\frac{-1-\sqrt{17}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{17}}{2*1}=\frac{-1+\sqrt{17}}{2}
$