X/x-8+6/x-4=x^2/x^2-12x+32

Solution for X/x-8+6/x-4=x^2/x^2-12x+32 equation:

X/X-8+6/X-4=X^2/X^2-12X+32

We move all terms to the left:

X/X-8+6/X-4-(X^2/X^2-12X+32)=0


Domain of the equation: X!=0

X∈R



Domain of the equation: X^2-12X+32)!=0

X∈R


We add all the numbers together, and all the variables

X/X+6/X-(X^2/X^2-12X+32)-12=0

We get rid of parentheses

-X^2/X^2+X/X+6/X+12X-32-12=0

Fractions to decimals

6/X+12X-32-12+1+1=0

We multiply all the terms by the denominator


12X*X-32*X-12*X+1*X+1*X+6=0

We add all the numbers together, and all the variables

-42X+12X*X+6=0

Wy multiply elements

12X^2-42X+6=0

a = 12; b = -42; c = +6;
Δ = b2-4ac
Δ = -422-4·12·6
Δ = 1476
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:

$\sqrt{\Delta}=\sqrt{1476}=\sqrt{36*41}=\sqrt{36}*\sqrt{41}=6\sqrt{41}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-6\sqrt{41}}{2*12}=\frac{42-6\sqrt{41}}{24}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+6\sqrt{41}}{2*12}=\frac{42+6\sqrt{41}}{24}
$