2x/x+9=x-2/x-1

Solution for 2x/x+9=x-2/x-1 equation:

2x/x+9=x-2/x-1

We move all terms to the left:

2x/x+9-(x-2/x-1)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: x-1)!=0

x∈R


We get rid of parentheses

2x/x-x+2/x+1+9=0

We multiply all the terms by the denominator


2x-x*x+1*x+9*x+2=0

We add all the numbers together, and all the variables

12x-x*x+2=0

Wy multiply elements

-1x^2+12x+2=0

a = -1; b = 12; c = +2;
Δ = b2-4ac
Δ = 122-4·(-1)·2
Δ = 152
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{152}=\sqrt{4*38}=\sqrt{4}*\sqrt{38}=2\sqrt{38}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{38}}{2*-1}=\frac{-12-2\sqrt{38}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{38}}{2*-1}=\frac{-12+2\sqrt{38}}{-2}
$