(1+x)/(1+x^2)=3/5

Solution for (1+x)/(1+x^2)=3/5 equation:

(1+x)/(1+x^2)=3/5

We move all terms to the left:

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


Domain of the equation: (1+x^2)!=0

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

x^2!=-1

x^2!=-1/

x^2!=√-1/

x!=NAN

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


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

We multiply all the terms by the denominator


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

We get rid of parentheses

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

We add all the numbers together, and all the variables

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

a = -3; b = 5; c = +2;
Δ = b2-4ac
Δ = 52-4·(-3)·2
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-7}{2*-3}=\frac{-12}{-6}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+7}{2*-3}=\frac{2}{-6}
=-1/3
$