2x+3/x+3=x+4/x+2

Solution for 2x+3/x+3=x+4/x+2 equation:

2x+3/x+3=x+4/x+2

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: x+2)!=0

x∈R


We get rid of parentheses

2x+3/x-x-4/x-2+3=0

We multiply all the terms by the denominator


2x*x-x*x-2*x+3*x+3-4=0

We add all the numbers together, and all the variables

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

Wy multiply elements

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

We add all the numbers together, and all the variables

x^2+x-1=0

a = 1; b = 1; c = -1;
Δ = b2-4ac
Δ = 12-4·1·(-1)
Δ = 5
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{-(1)-\sqrt{5}}{2*1}=\frac{-1-\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{5}}{2*1}=\frac{-1+\sqrt{5}}{2}
$