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

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

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

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(-6x+3)/2x^2+(-5x)/2x^2+1=0

We multiply all the terms by the denominator


(-6x+3)+(-5x)+1*2x^2=0

Wy multiply elements

2x^2+(-6x+3)+(-5x)=0

We get rid of parentheses

2x^2-6x-5x+3=0

We add all the numbers together, and all the variables

2x^2-11x+3=0

a = 2; b = -11; c = +3;
Δ = b2-4ac
Δ = -112-4·2·3
Δ = 97
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-\sqrt{97}}{2*2}=\frac{11-\sqrt{97}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{97}}{2*2}=\frac{11+\sqrt{97}}{4}
$