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

Solution for X+6/x-4=1/x+1 equation:

X+6/X-4=1/X+1

We move all terms to the left:

X+6/X-4-(1/X+1)=0


Domain of the equation: X!=0

X∈R



Domain of the equation: X+1)!=0

X∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

-5X+X*X+5=0

Wy multiply elements

X^2-5X+5=0

a = 1; b = -5; c = +5;
Δ = b2-4ac
Δ = -52-4·1·5
Δ = 5
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{-(-5)-\sqrt{5}}{2*1}=\frac{5-\sqrt{5}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{5}}{2*1}=\frac{5+\sqrt{5}}{2}
$