X-1/x-9+1/x-3=2/x+3

Solution for X-1/x-9+1/x-3=2/x+3 equation:

X-1/X-9+1/X-3=2/X+3

We move all terms to the left:

X-1/X-9+1/X-3-(2/X+3)=0


Domain of the equation: X!=0

X∈R



Domain of the equation: X+3)!=0

X∈R


We add all the numbers together, and all the variables

X-1/X+1/X-(2/X+3)-12=0

We get rid of parentheses

X-1/X+1/X-2/X-3-12=0

We multiply all the terms by the denominator


X*X-3*X-12*X-1+1-2=0

We add all the numbers together, and all the variables

-15X+X*X-2=0

Wy multiply elements

X^2-15X-2=0

a = 1; b = -15; c = -2;
Δ = b2-4ac
Δ = -152-4·1·(-2)
Δ = 233
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{-(-15)-\sqrt{233}}{2*1}=\frac{15-\sqrt{233}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{233}}{2*1}=\frac{15+\sqrt{233}}{2}
$