5/3x+1=4/x+2

Solution for 5/3x+1=4/x+2 equation:

5/3x+1=4/x+2

We move all terms to the left:

5/3x+1-(4/x+2)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



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

x∈R


We get rid of parentheses

5/3x-4/x-2+1=0

We calculate fractions


5x/3x^2+(-12x)/3x^2-2+1=0

We add all the numbers together, and all the variables

5x/3x^2+(-12x)/3x^2-1=0

We multiply all the terms by the denominator


5x+(-12x)-1*3x^2=0

Wy multiply elements

-3x^2+5x+(-12x)=0

We get rid of parentheses

-3x^2+5x-12x=0

We add all the numbers together, and all the variables

-3x^2-7x=0

a = -3; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·(-3)·0
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{-(-7)-7}{2*-3}=\frac{0}{-6}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*-3}=\frac{14}{-6}
=-2+1/3
$