x-5/x-8=1/x

Solution for x-5/x-8=1/x equation:

x-5/x-8=1/x

We move all terms to the left:

x-5/x-8-(1/x)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x-5/x-(+1/x)-8=0

We get rid of parentheses

x-5/x-1/x-8=0

We multiply all the terms by the denominator


x*x-8*x-5-1=0

We add all the numbers together, and all the variables

-8x+x*x-6=0

Wy multiply elements

x^2-8x-6=0

a = 1; b = -8; c = -6;
Δ = b2-4ac
Δ = -82-4·1·(-6)
Δ = 88
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:

$\sqrt{\Delta}=\sqrt{88}=\sqrt{4*22}=\sqrt{4}*\sqrt{22}=2\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{22}}{2*1}=\frac{8-2\sqrt{22}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{22}}{2*1}=\frac{8+2\sqrt{22}}{2}
$