1/x-2+1/x+3=4/x+x+x-6

Solution for 1/x-2+1/x+3=4/x+x+x-6 equation:

1/x-2+1/x+3=4/x+x+x-6

We move all terms to the left:

1/x-2+1/x+3-(4/x+x+x-6)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: x+x+x-6)!=0

x∈R


We add all the numbers together, and all the variables

1/x+1/x-(2x+4/x-6)-2+3=0

We add all the numbers together, and all the variables

1/x+1/x-(2x+4/x-6)+1=0

We get rid of parentheses

1/x+1/x-2x-4/x+6+1=0

We multiply all the terms by the denominator


-2x*x+6*x+1*x+1+1-4=0

We add all the numbers together, and all the variables

7x-2x*x-2=0

Wy multiply elements

-2x^2+7x-2=0

a = -2; b = 7; c = -2;
Δ = b2-4ac
Δ = 72-4·(-2)·(-2)
Δ = 33
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{-(7)-\sqrt{33}}{2*-2}=\frac{-7-\sqrt{33}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{33}}{2*-2}=\frac{-7+\sqrt{33}}{-4}
$