w/w-1+w=4w-3/w-1

Solution for w/w-1+w=4w-3/w-1 equation:

w/w-1+w=4w-3/w-1

We move all terms to the left:

w/w-1+w-(4w-3/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

w+w/w-(4w-3/w-1)-1=0

We get rid of parentheses

w+w/w-4w+3/w+1-1=0

Fractions to decimals

3/w+w-4w+1-1+1=0

We multiply all the terms by the denominator


w*w-4w*w+1*w-1*w+1*w+3=0

We add all the numbers together, and all the variables

w+w*w-4w*w+3=0

Wy multiply elements

w^2-4w^2+w+3=0

We add all the numbers together, and all the variables

-3w^2+w+3=0

a = -3; b = 1; c = +3;
Δ = b2-4ac
Δ = 12-4·(-3)·3
Δ = 37
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{37}}{2*-3}=\frac{-1-\sqrt{37}}{-6}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{37}}{2*-3}=\frac{-1+\sqrt{37}}{-6}
$