a-2/a+3-1=3/a+2

Solution for a-2/a+3-1=3/a+2 equation:

a-2/a+3-1=3/a+2

We move all terms to the left:

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


Domain of the equation: a!=0

a∈R



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

a∈R


We add all the numbers together, and all the variables

a-2/a-(3/a+2)+2=0

We get rid of parentheses

a-2/a-3/a-2+2=0

We multiply all the terms by the denominator


a*a-2*a+2*a-2-3=0

We add all the numbers together, and all the variables

a*a-5=0

Wy multiply elements

a^2-5=0

a = 1; b = 0; c = -5;
Δ = b2-4ac
Δ = 02-4·1·(-5)
Δ = 20
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{20}=\sqrt{4*5}=\sqrt{4}*\sqrt{5}=2\sqrt{5}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{5}}{2*1}=\frac{0-2\sqrt{5}}{2}
=-\frac{2\sqrt{5}}{2}
=-\sqrt{5}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{5}}{2*1}=\frac{0+2\sqrt{5}}{2}
=\frac{2\sqrt{5}}{2}
=\sqrt{5}
$