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

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

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

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


x-x+(-3x)/5x^2+(-10x)/5x^2+1=0

We add all the numbers together, and all the variables

(-3x)/5x^2+(-10x)/5x^2+1=0

We multiply all the terms by the denominator


(-3x)+(-10x)+1*5x^2=0

Wy multiply elements

5x^2+(-3x)+(-10x)=0

We get rid of parentheses

5x^2-3x-10x=0

We add all the numbers together, and all the variables

5x^2-13x=0

a = 5; b = -13; c = 0;
Δ = b2-4ac
Δ = -132-4·5·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-13}{2*5}=\frac{0}{10}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+13}{2*5}=\frac{26}{10}
=2+3/5
$