11+1/3x=1/x

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

11+1/3x=1/x

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

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

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

We get rid of parentheses

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

We calculate fractions


x/3x^2+(-3x)/3x^2+11=0

We multiply all the terms by the denominator


x+(-3x)+11*3x^2=0

Wy multiply elements

33x^2+x+(-3x)=0

We get rid of parentheses

33x^2+x-3x=0

We add all the numbers together, and all the variables

33x^2-2x=0

a = 33; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·33·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*33}=\frac{0}{66}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*33}=\frac{4}{66}
=2/33
$