X/x-1=2x+10/x+11

Solution for X/x-1=2x+10/x+11 equation:

X/X-1=2X+10/X+11

We move all terms to the left:

X/X-1-(2X+10/X+11)=0


Domain of the equation: X!=0

X∈R



Domain of the equation: X+11)!=0

X∈R


We get rid of parentheses

X/X-2X-10/X-11-1=0

Fractions to decimals

-10/X-2X-11-1+1=0

We multiply all the terms by the denominator


-2X*X-11*X-1*X+1*X-10=0

We add all the numbers together, and all the variables

-11X-2X*X-10=0

Wy multiply elements

-2X^2-11X-10=0

a = -2; b = -11; c = -10;
Δ = b2-4ac
Δ = -112-4·(-2)·(-10)
Δ = 41
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{-(-11)-\sqrt{41}}{2*-2}=\frac{11-\sqrt{41}}{-4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{41}}{2*-2}=\frac{11+\sqrt{41}}{-4}
$