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

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

X+2/X-1+X-1/X+2=5/2

We move all terms to the left:

X+2/X-1+X-1/X+2-(5/2)=0


Domain of the equation: X!=0

X∈R


We add all the numbers together, and all the variables

X+2/X+X-1/X-1+2-(+5/2)=0

We add all the numbers together, and all the variables

2X+2/X-1/X+1-(+5/2)=0

We get rid of parentheses

2X+2/X-1/X+1-5/2=0

We calculate fractions


2X+()/2X+(-5X)/2X+1=0

We multiply all the terms by the denominator


2X*2X+(-5X)+1*2X+()=0

We add all the numbers together, and all the variables

2X*2X+(-5X)+1*2X=0

Wy multiply elements

4X^2+(-5X)+2X=0

We get rid of parentheses

4X^2-5X+2X=0

We add all the numbers together, and all the variables

4X^2-3X=0

a = 4; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·4·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*4}=\frac{0}{8}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*4}=\frac{6}{8}
=3/4
$