x+2/x+6=x/x+3

Solution for x+2/x+6=x/x+3 equation:

x+2/x+6=x/x+3

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: x+3)!=0

x∈R


We get rid of parentheses

x+2/x-x/x-3+6=0

Fractions to decimals

2/x+x-3+6+1=0

We multiply all the terms by the denominator


x*x-3*x+6*x+1*x+2=0

We add all the numbers together, and all the variables

4x+x*x+2=0

Wy multiply elements

x^2+4x+2=0

a = 1; b = 4; c = +2;
Δ = b2-4ac
Δ = 42-4·1·2
Δ = 8
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:

$\sqrt{\Delta}=\sqrt{8}=\sqrt{4*2}=\sqrt{4}*\sqrt{2}=2\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{2}}{2*1}=\frac{-4-2\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{2}}{2*1}=\frac{-4+2\sqrt{2}}{2}
$