x-5/x+1=3

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

x-5/x+1=3

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

x-5/x-2=0

We multiply all the terms by the denominator


x*x-2*x-5=0

We add all the numbers together, and all the variables

-2x+x*x-5=0

Wy multiply elements

x^2-2x-5=0

a = 1; b = -2; c = -5;
Δ = b2-4ac
Δ = -22-4·1·(-5)
Δ = 24
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:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{6}}{2*1}=\frac{2-2\sqrt{6}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{6}}{2*1}=\frac{2+2\sqrt{6}}{2}
$