x+4/x+1=3x+4/x+3

Solution for x+4/x+1=3x+4/x+3 equation:

x+4/x+1=3x+4/x+3

We move all terms to the left:

x+4/x+1-(3x+4/x+3)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: x+3)!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

-2x+x*x-3x*x=0

Wy multiply elements

x^2-3x^2-2x=0

We add all the numbers together, and all the variables

-2x^2-2x=0

a = -2; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·(-2)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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