X+1=-3x+5/x+1

Solution for X+1=-3x+5/x+1 equation:

X+1=-3X+5/X+1

We move all terms to the left:

X+1-(-3X+5/X+1)=0


Domain of the equation: X+1)!=0

X∈R


We get rid of parentheses

X+3X-5/X-1+1=0

We multiply all the terms by the denominator


X*X+3X*X-1*X+1*X-5=0

We add all the numbers together, and all the variables

X*X+3X*X-5=0

Wy multiply elements

X^2+3X^2-5=0

We add all the numbers together, and all the variables

4X^2-5=0

a = 4; b = 0; c = -5;
Δ = b2-4ac
Δ = 02-4·4·(-5)
Δ = 80
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{5}}{2*4}=\frac{0-4\sqrt{5}}{8}
=-\frac{4\sqrt{5}}{8}
=-\frac{\sqrt{5}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{5}}{2*4}=\frac{0+4\sqrt{5}}{8}
=\frac{4\sqrt{5}}{8}
=\frac{\sqrt{5}}{2}
$