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

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

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

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x-5)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

(-2x)/2x^2+(-3x)/2x^2+3=0

We multiply all the terms by the denominator


(-2x)+(-3x)+3*2x^2=0

Wy multiply elements

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

6x^2-5x=0

a = 6; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·6·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*6}=\frac{0}{12}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*6}=\frac{10}{12}
=5/6
$