Question

solve the equation...
x^2 64
---- = ----
x-8 x-8

Answer 1

this is pretty simple because they have the same denominator, you know that the numerators must be equal.
given that,
x^2=64, and the square root of 64 is 8 OR -8. Now plug each of these into the equation to see if it works.

for 8,

you plug it in and have
8^2/(8-8)=64/(8-8)
BUT 8-8 =0 and you cannot divide by 0. so you know 8 does not work.

now testing with -8
(-8)^2/(-8-8)=64/(-8-8)
64/(-16)=64/(-16) which is TRUE.

So your answer is -8.

Answer 2

\[x= \pm8\]

Answer 3

x*2 /(x-8) =64/(x-8) --- x*2 =64 --- x*2 =8*2 --- x_1=64*(1/2) =8 and
x_2 =64*(1/2) =-8