3/a+1=a+3/a

Solution for 3/a+1=a+3/a equation:

3/a+1=a+3/a

We move all terms to the left:

3/a+1-(a+3/a)=0


Domain of the equation: a!=0

a∈R



Domain of the equation: a)!=0

a!=0/1

a!=0

a∈R


We add all the numbers together, and all the variables

3/a-(+a+3/a)+1=0

We get rid of parentheses

3/a-a-3/a+1=0

We multiply all the terms by the denominator


-a*a+1*a+3-3=0

We add all the numbers together, and all the variables

a-a*a=0

Wy multiply elements

-1a^2+a=0

a = -1; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-1)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*-1}=\frac{-2}{-2}
=1
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-1}=\frac{0}{-2}
=0
$