(x-0.5)/(x+0.5)=2x/x-2

Solution for (x-0.5)/(x+0.5)=2x/x-2 equation:

(x-0.5)/(x+0.5)=2x/x-2

We move all terms to the left:

(x-0.5)/(x+0.5)-(2x/x-2)=0


Domain of the equation: (x+0.5)!=0

We move all terms containing x to the left, all other terms to the right

x!=-0.5

x∈R



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

x∈R


We get rid of parentheses

(x-0.5)/(x+0.5)-2x/x+2=0

We calculate fractions


(-2x^2-1x)/(x^2+0.5x)+(x^2-0.5x)/(x^2+0.5x)+2=0

We multiply all the terms by the denominator


(-2x^2-1x)+(x^2-0.5x)+2*(x^2+0.5x)=0

We multiply parentheses

(-2x^2-1x)+2x^2+(x^2-0.5x)+0x=0

We get rid of parentheses

-2x^2+2x^2+x^2-1x-0.5x+0x=0

We add all the numbers together, and all the variables

x^2-0.5x=0

a = 1; b = -0.5; c = 0;
Δ = b2-4ac
Δ = -0.52-4·1·0
Δ = 0.25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-0.5)-\sqrt{0.25}}{2*1}=\frac{0.5-\sqrt{0.25}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.5)+\sqrt{0.25}}{2*1}=\frac{0.5+\sqrt{0.25}}{2}
$