3/x+1-5=x-11/x+1

Solution for 3/x+1-5=x-11/x+1 equation:

3/x+1-5=x-11/x+1

We move all terms to the left:

3/x+1-5-(x-11/x+1)=0


Domain of the equation: x!=0

x∈R



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

x∈R


We add all the numbers together, and all the variables

3/x-(x-11/x+1)-4=0

We get rid of parentheses

3/x-x+11/x-1-4=0

We multiply all the terms by the denominator


-x*x-1*x-4*x+3+11=0

We add all the numbers together, and all the variables

-5x-x*x+14=0

Wy multiply elements

-1x^2-5x+14=0

a = -1; b = -5; c = +14;
Δ = b2-4ac
Δ = -52-4·(-1)·14
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-9}{2*-1}=\frac{-4}{-2}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+9}{2*-1}=\frac{14}{-2}
=-7
$