X+9/x-2+1=11/x-2

Solution for X+9/x-2+1=11/x-2 equation:

X+9/X-2+1=11/X-2

We move all terms to the left:

X+9/X-2+1-(11/X-2)=0


Domain of the equation: X!=0

X∈R



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

X∈R


We add all the numbers together, and all the variables

X+9/X-(11/X-2)-1=0

We get rid of parentheses

X+9/X-11/X+2-1=0

We multiply all the terms by the denominator


X*X+2*X-1*X+9-11=0

We add all the numbers together, and all the variables

X+X*X-2=0

Wy multiply elements

X^2+X-2=0

a = 1; b = 1; c = -2;
Δ = b2-4ac
Δ = 12-4·1·(-2)
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{-(1)-3}{2*1}=\frac{-4}{2}
=-2
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+3}{2*1}=\frac{2}{2}
=1
$