Answer:
[tex]x=5[/tex]
Step-by-step explanation:
We are given
[tex]\frac{x-2}{x-4} =\frac{x+4}{x-2}[/tex]
Since, we have to solve for x
so, we will try to get rid of x on any one side
We can cross multiply both sides
[tex](x-2)\times (x-2)=(x-4)\times (x+4)[/tex]
now, we can simplify it
[tex]x^2-4x+4=x^2-16[/tex]
Subtract both sides by x^2
[tex]x^2-4x+4-x^2=x^2-16-x^2[/tex]
[tex]-4x+4=-16[/tex]
Subtract both sides by 4
[tex]-4x+4-4=-16-4[/tex]
[tex]-4x=-20[/tex]
Divide both sides by -4
and we get
[tex]x=5[/tex]
