3y+4/y-1=7/y-1

Solution for 3y+4/y-1=7/y-1 equation:

3y+4/y-1=7/y-1

We move all terms to the left:

3y+4/y-1-(7/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

3y+4/y-7/y+1-1=0

We multiply all the terms by the denominator


3y*y+1*y-1*y+4-7=0

We add all the numbers together, and all the variables

3y*y-3=0

Wy multiply elements

3y^2-3=0

a = 3; b = 0; c = -3;
Δ = b2-4ac
Δ = 02-4·3·(-3)
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6}{2*3}=\frac{-6}{6}
=-1
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6}{2*3}=\frac{6}{6}
=1
$