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

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

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

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



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

x∈R


We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-10x^2-2x=0

a = -10; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·(-10)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*-10}=\frac{0}{-20}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*-10}=\frac{4}{-20}
=-1/5
$