X/x+3=x+1/x-5

Solution for X/x+3=x+1/x-5 equation:

X/X+3=X+1/X-5

We move all terms to the left:

X/X+3-(X+1/X-5)=0


Domain of the equation: X!=0

X∈R



Domain of the equation: X-5)!=0

X∈R


We get rid of parentheses

X/X-X-1/X+5+3=0

Fractions to decimals

-1/X-X+5+3+1=0

We multiply all the terms by the denominator


-X*X+5*X+3*X+1*X-1=0

We add all the numbers together, and all the variables

9X-X*X-1=0

Wy multiply elements

-1X^2+9X-1=0

a = -1; b = 9; c = -1;
Δ = b2-4ac
Δ = 92-4·(-1)·(-1)
Δ = 77
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{-(9)-\sqrt{77}}{2*-1}=\frac{-9-\sqrt{77}}{-2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{77}}{2*-1}=\frac{-9+\sqrt{77}}{-2}
$