3y-4/y-1=7/y-1+2

Solution for 3y-4/y-1=7/y-1+2 equation:

3y-4/y-1=7/y-1+2

We move all terms to the left:

3y-4/y-1-(7/y-1+2)=0


Domain of the equation: y!=0

y∈R



Domain of the equation: y-1+2)!=0

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

y+2)!=1

y∈R


We add all the numbers together, and all the variables

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

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

-2y+3y*y-11=0

Wy multiply elements

3y^2-2y-11=0

a = 3; b = -2; c = -11;
Δ = b2-4ac
Δ = -22-4·3·(-11)
Δ = 136
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:

$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{34}}{2*3}=\frac{2-2\sqrt{34}}{6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{34}}{2*3}=\frac{2+2\sqrt{34}}{6}
$