X+8/x-2=2x+3/x+5

Solution for X+8/x-2=2x+3/x+5 equation:

X+8/X-2=2X+3/X+5

We move all terms to the left:

X+8/X-2-(2X+3/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+8/X-2X-3/X-5-2=0

We multiply all the terms by the denominator


X*X-2X*X-5*X-2*X+8-3=0

We add all the numbers together, and all the variables

-7X+X*X-2X*X+5=0

Wy multiply elements

X^2-2X^2-7X+5=0

We add all the numbers together, and all the variables

-1X^2-7X+5=0

a = -1; b = -7; c = +5;
Δ = b2-4ac
Δ = -72-4·(-1)·5
Δ = 69
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{-(-7)-\sqrt{69}}{2*-1}=\frac{7-\sqrt{69}}{-2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{69}}{2*-1}=\frac{7+\sqrt{69}}{-2}
$