1/x+5=x-3/x

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

1/x+5=x-3/x

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


-x*x+5*x+1+3=0

We add all the numbers together, and all the variables

5x-x*x+4=0

Wy multiply elements

-1x^2+5x+4=0

a = -1; b = 5; c = +4;
Δ = b2-4ac
Δ = 52-4·(-1)·4
Δ = 41
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{-(5)-\sqrt{41}}{2*-1}=\frac{-5-\sqrt{41}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{41}}{2*-1}=\frac{-5+\sqrt{41}}{-2}
$