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

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

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

We move all terms to the left:

5x/x+1-1-(x+1/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

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

5x/x-x-1/x=0

We multiply all the terms by the denominator


5x-x*x-1=0

Wy multiply elements

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

a = -1; b = 5; c = -1;
Δ = b2-4ac
Δ = 52-4·(-1)·(-1)
Δ = 21
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{21}}{2*-1}=\frac{-5-\sqrt{21}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{21}}{2*-1}=\frac{-5+\sqrt{21}}{-2}
$