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How much work must be done on a particle with a mass of m to accelerate it from rest to a speed of v_1? (Express the answer in terms of mc^2.)

I figured that this would just be the kenetic energy which is givin by

K= mc^2/(sqrt(1-(v/c)^2) - mc^2

so i factored out an mc^2 and was left with

work= (1/sqrt(1-(v/c)^2) -1)*mc^2

but mastering physics says that the answer does not depend on c.

i dont see how this is possible

thanks for the help