1-x/x+1+3=2x+3/x+1

Solution for 1-x/x+1+3=2x+3/x+1 equation:

1-x/x+1+3=2x+3/x+1

We move all terms to the left:

1-x/x+1+3-(2x+3/x+1)=0


Domain of the equation: x!=0

x∈R



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

x∈R


We add all the numbers together, and all the variables

-x/x-(2x+3/x+1)+5=0

We get rid of parentheses

-x/x-2x-3/x-1+5=0

Fractions to decimals

-3/x-2x-1+5+1=0

We multiply all the terms by the denominator


-2x*x-1*x+5*x+1*x-3=0

We add all the numbers together, and all the variables

5x-2x*x-3=0

Wy multiply elements

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

a = -2; b = 5; c = -3;
Δ = b2-4ac
Δ = 52-4·(-2)·(-3)
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-1}{2*-2}=\frac{-6}{-4}
=1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+1}{2*-2}=\frac{-4}{-4}
=1
$