Write a rational Algebraic Equation that has extraneous solutions of 0 and 6

Answer 1

extraneous solutions of 0 and 6

x(x-6) = 0 with solutions 0 and 6

go backwards, retro reverse engineer to

what you had before multiplying by a common denominator

0/(x-6) = 1/x

has solution x= 6, if you

multiply by common denominator (x)(x-6)

or cross multiply to get

0 = x-6

x=6

but 6 is not a solution of the original equation as it make the left side undefined with division by 0

0 also can't be a solution as it makes the right side undefined with division by 0 prohibited

so retro reverse further into the past, into the twilight zone back like the Cal Tech Big Bang Professors with their Time Machine, led by Prof Sheldon Cooper. Go back wards in time, like Stephan Hawkings or Albert Einstein, the scientific approach, super science, beyond mere science into other dimensions like Capt Kirk and the Enterprise where no man has gone before

got a little side tracked. but follow the ball, watch the ball like Robert Redford in the movie "Natural" or one of those baseball movies. Okay not Natural but the movie about "Produce" the best grocery worker ever. what's the movie name? good movie. the super star tells Produce keep your eye on the ball. Major baseball advice to a batter, which has become a platitude maxim for life

try

0/(x^2-6x) = 1/x^2