y-3/y-1=4/y-1

Solution for y-3/y-1=4/y-1 equation:

y-3/y-1=4/y-1

We move all terms to the left:

y-3/y-1-(4/y-1)=0


Domain of the equation: y!=0

y∈R



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

y∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

y*y-7=0

Wy multiply elements

y^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:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

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