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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

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

We calculate fractions


x^2/2x^2+8x/2x^2-3=0

We multiply all the terms by the denominator


x^2+8x-3*2x^2=0

Wy multiply elements

x^2-6x^2+8x=0

We add all the numbers together, and all the variables

-5x^2+8x=0

a = -5; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·(-5)·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8}{2*-5}=\frac{-16}{-10}
=1+3/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*-5}=\frac{0}{-10}
=0
$