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

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

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

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



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

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


5x*x-1*x+1*x-2-4=0

We add all the numbers together, and all the variables

5x*x-6=0

Wy multiply elements

5x^2-6=0

a = 5; b = 0; c = -6;
Δ = b2-4ac
Δ = 02-4·5·(-6)
Δ = 120
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:

$\sqrt{\Delta}=\sqrt{120}=\sqrt{4*30}=\sqrt{4}*\sqrt{30}=2\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{30}}{2*5}=\frac{0-2\sqrt{30}}{10}
=-\frac{2\sqrt{30}}{10}
=-\frac{\sqrt{30}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{30}}{2*5}=\frac{0+2\sqrt{30}}{10}
=\frac{2\sqrt{30}}{10}
=\frac{\sqrt{30}}{5}
$