12/x+24/(x-1)=11

Solution for 12/x+24/(x-1)=11 equation:

12/x+24/(x-1)=11

We move all terms to the left:

12/x+24/(x-1)-(11)=0


Domain of the equation: x!=0

x∈R



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

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

x!=1

x∈R


We calculate fractions


(12x-12)/(x^2-1x)+24x/(x^2-1x)-11=0

We multiply all the terms by the denominator


(12x-12)+24x-11*(x^2-1x)=0

We add all the numbers together, and all the variables

24x+(12x-12)-11*(x^2-1x)=0

We multiply parentheses

-11x^2+24x+(12x-12)+11x=0

We get rid of parentheses

-11x^2+24x+12x+11x-12=0

We add all the numbers together, and all the variables

-11x^2+47x-12=0

a = -11; b = 47; c = -12;
Δ = b2-4ac
Δ = 472-4·(-11)·(-12)
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(47)-41}{2*-11}=\frac{-88}{-22}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(47)+41}{2*-11}=\frac{-6}{-22}
=3/11
$