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

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

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

We move all terms to the left:

x+3/5x-2-(x/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

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

Fractions to decimals

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

5x^2-10x+3=0

a = 5; b = -10; c = +3;
Δ = b2-4ac
Δ = -102-4·5·3
Δ = 40
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{10}}{2*5}=\frac{10-2\sqrt{10}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{10}}{2*5}=\frac{10+2\sqrt{10}}{10}
$