(x-1/x-6)-(6/x-4)=1

Solution for (x-1/x-6)-(6/x-4)=1 equation:

(x-1/x-6)-(6/x-4)=1

We move all terms to the left:

(x-1/x-6)-(6/x-4)-(1)=0


Domain of the equation: x-6)!=0

x∈R



Domain of the equation: x-4)!=0

x∈R


We get rid of parentheses

x-1/x-6/x-6+4-1=0

We multiply all the terms by the denominator


x*x-6*x+4*x-1*x-1-6=0

We add all the numbers together, and all the variables

-3x+x*x-7=0

Wy multiply elements

x^2-3x-7=0

a = 1; b = -3; c = -7;
Δ = b2-4ac
Δ = -32-4·1·(-7)
Δ = 37
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{-(-3)-\sqrt{37}}{2*1}=\frac{3-\sqrt{37}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{37}}{2*1}=\frac{3+\sqrt{37}}{2}
$