X-1/x-2=-5/x-8

Solution for X-1/x-2=-5/x-8 equation:

X-1/X-2=-5/X-8

We move all terms to the left:

X-1/X-2-(-5/X-8)=0


Domain of the equation: X!=0

X∈R



Domain of the equation: X-8)!=0

X∈R


We get rid of parentheses

X-1/X+5/X+8-2=0

We multiply all the terms by the denominator


X*X+8*X-2*X-1+5=0

We add all the numbers together, and all the variables

6X+X*X+4=0

Wy multiply elements

X^2+6X+4=0

a = 1; b = 6; c = +4;
Δ = b2-4ac
Δ = 62-4·1·4
Δ = 20
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:

$\sqrt{\Delta}=\sqrt{20}=\sqrt{4*5}=\sqrt{4}*\sqrt{5}=2\sqrt{5}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{5}}{2*1}=\frac{-6-2\sqrt{5}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{5}}{2*1}=\frac{-6+2\sqrt{5}}{2}
$