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

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

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

We move all terms to the left:

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


Domain of the equation: Y!=0

Y∈R



Domain of the equation: Y+3+1)!=0

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

Y+1)!=-3

Y∈R


We add all the numbers together, and all the variables

-2/Y-(Y-7/Y+4)+4=0

We get rid of parentheses

-2/Y-Y+7/Y-4+4=0

We multiply all the terms by the denominator


-Y*Y-4*Y+4*Y-2+7=0

We add all the numbers together, and all the variables

-Y*Y+5=0

Wy multiply elements

-1Y^2+5=0

a = -1; b = 0; c = +5;
Δ = b2-4ac
Δ = 02-4·(-1)·5
Δ = 20
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:

$\sqrt{\Delta}=\sqrt{20}=\sqrt{4*5}=\sqrt{4}*\sqrt{5}=2\sqrt{5}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{5}}{2*-1}=\frac{0-2\sqrt{5}}{-2}
=-\frac{2\sqrt{5}}{-2}
=-\frac{\sqrt{5}}{-1}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{5}}{2*-1}=\frac{0+2\sqrt{5}}{-2}
=\frac{2\sqrt{5}}{-2}
=\frac{\sqrt{5}}{-1}
$