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

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

X+2/3X-1+1=6-X/X+1

We move all terms to the left:

X+2/3X-1+1-(6-X/X+1)=0


Domain of the equation: 3X!=0

X!=0/3

X!=0

X∈R



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

X∈R


We add all the numbers together, and all the variables

X+2/3X-(-X/X+7)-1+1=0

We add all the numbers together, and all the variables

X+2/3X-(-X/X+7)=0

We get rid of parentheses

X+2/3X+X/X-7=0

Fractions to decimals

2/3X+X-7+1=0

We multiply all the terms by the denominator


X*3X-7*3X+1*3X+2=0

Wy multiply elements

3X^2-21X+3X+2=0

We add all the numbers together, and all the variables

3X^2-18X+2=0

a = 3; b = -18; c = +2;
Δ = b2-4ac
Δ = -182-4·3·2
Δ = 300
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{300}=\sqrt{100*3}=\sqrt{100}*\sqrt{3}=10\sqrt{3}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-10\sqrt{3}}{2*3}=\frac{18-10\sqrt{3}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+10\sqrt{3}}{2*3}=\frac{18+10\sqrt{3}}{6}
$