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

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

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

We move all terms to the left:

w+3/w-1+w+5/w-(3w+1/w-1)=0


Domain of the equation: w!=0

w∈R



Domain of the equation: w-1)!=0

w∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

2w+3/w+5/w-3w-1/w+1-1=0

We multiply all the terms by the denominator


2w*w-3w*w+1*w-1*w+3+5-1=0

We add all the numbers together, and all the variables

2w*w-3w*w+7=0

Wy multiply elements

2w^2-3w^2+7=0

We add all the numbers together, and all the variables

-1w^2+7=0

a = -1; b = 0; c = +7;
Δ = b2-4ac
Δ = 02-4·(-1)·7
Δ = 28
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:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{7}}{2*-1}=\frac{0-2\sqrt{7}}{-2}
=-\frac{2\sqrt{7}}{-2}
=-\frac{\sqrt{7}}{-1}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{7}}{2*-1}=\frac{0+2\sqrt{7}}{-2}
=\frac{2\sqrt{7}}{-2}
=\frac{\sqrt{7}}{-1}
$