2r+1/r+3=1+r+3/r+1

Solution for 2r+1/r+3=1+r+3/r+1 equation:

2r+1/r+3=1+r+3/r+1

We move all terms to the left:

2r+1/r+3-(1+r+3/r+1)=0


Domain of the equation: r!=0

r∈R



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

r∈R


We add all the numbers together, and all the variables

2r+1/r-(r+3/r+2)+3=0

We get rid of parentheses

2r+1/r-r-3/r-2+3=0

We multiply all the terms by the denominator


2r*r-r*r-2*r+3*r+1-3=0

We add all the numbers together, and all the variables

r+2r*r-r*r-2=0

Wy multiply elements

2r^2-1r^2+r-2=0

We add all the numbers together, and all the variables

r^2+r-2=0

a = 1; b = 1; c = -2;
Δ = b2-4ac
Δ = 12-4·1·(-2)
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-3}{2*1}=\frac{-4}{2}
=-2
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+3}{2*1}=\frac{2}{2}
=1
$