W-1/w+2=w-5/w+3+1

Solution for W-1/w+2=w-5/w+3+1 equation:

-1/W+2=W-5/W+3+1

We move all terms to the left:

-1/W+2-(W-5/W+3+1)=0


Domain of the equation: W!=0

W∈R



Domain of the equation: W+3+1)!=0

We move all terms containing W to the left, all other terms to the right

W+1)!=-3

W∈R


We add all the numbers together, and all the variables

-1/W-(W-5/W+4)+2=0

We get rid of parentheses

-1/W-W+5/W-4+2=0

We multiply all the terms by the denominator


-W*W-4*W+2*W-1+5=0

We add all the numbers together, and all the variables

-2W-W*W+4=0

Wy multiply elements

-1W^2-2W+4=0

a = -1; b = -2; c = +4;
Δ = b2-4ac
Δ = -22-4·(-1)·4
Δ = 20
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$W_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$W_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

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