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

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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} $

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