Show work / explain it

X 1 = -4,X 2 =12

EXPLANATION:

Determine the defined range
X+6/x=6/x-8,x#0,x#8

Simplify the equation using cross-multiplication
(X+6) x (x-8)=6x

Move variable to the left-hand side and change its sign
(X-6)x(x-8)-6x=0

Multiply the parentheses
X^2-8x+6x-48-6x=0

Since two opposites add up to zero, remove them from the expression
X^2-8x-48=0

Write -8x as a difference
X^2+4x-12x-48=0

Factor out x from the expression
Xx(x+4)-12x-48=0

Factor out -12 from the expression
Xx(x+4)-12(x+4)=0

Factor out from the expression
(x+4)x(x-12)=0

When the product of factors equals 0, at least one factor is 0
x+4=0
x-12=0

Solve the equation for x
X=-4
X-12=0
X=-4,x#0,x#8

Check if the solution is in the defined range
X=-4
x=12

The equation has 2 solutions

X 1 = -4,X 2 =12

Hope this helps