x+3-(4/x-1)=5

Solution for x+3-(4/x-1)=5 equation:

x+3-(4/x-1)=5

We move all terms to the left:

x+3-(4/x-1)-(5)=0


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

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

x-4/x+1-2=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

-1x+x*x-4=0

Wy multiply elements

x^2-1x-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}
$