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

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

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

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



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

x∈R


We add all the numbers together, and all the variables

3x-1/x-(4x/x-3)+6=0

We get rid of parentheses

3x-1/x-4x/x+3+6=0

We multiply all the terms by the denominator


3x*x-4x+3*x+6*x-1=0

We add all the numbers together, and all the variables

5x+3x*x-1=0

Wy multiply elements

3x^2+5x-1=0

a = 3; b = 5; c = -1;
Δ = b2-4ac
Δ = 52-4·3·(-1)
Δ = 37
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{37}}{2*3}=\frac{-5-\sqrt{37}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{37}}{2*3}=\frac{-5+\sqrt{37}}{6}
$