請問~~~ [(3^4+4)/(5^4+4)] x [(7^4+4)/(9^4+4)] x [(11^4+4)/(13^4+4)] x ...... x [(51^4+4)/(53^4+4)] 化為最簡分數。 謝謝~~~?

Sol
x^4+4
=(x^4+4x^2+4)－4x^2
=(x^2－2x+2)(x^2+2x+2)
=[(x-1)^2+1]*[(x+1)^2+1]
So
[(3^4+4)/(5^4+4)]*[(7^4+4)/(9^4+4)]*[(11^4+4)/(13^4+4)]*…
*[(51^4+4)/(53^4+4)]
=[(3-1)^2+1]*[(3+1)^2+1]/｛[5-1)^2+1]*[(5+1)^2+1]｝
*[(7-1)^2+1]*[(7+1)^2+1]/｛[9-1)^2+1]*[(9+1)^2+1]｝
*[(11-1)^2+1]*[(11+1)^2+1]/｛[13-1)^2+1]*[(13+1)^2+1]｝
…….
*[(47-1)^2+1]*[(47+1)^2+1]/｛[(49-1)^2+1]*[(49+1)^2+1]｝
*[(51-1)^2+1]*[(51+1)^2+1]/｛[(53-1)^2+1]*[(53+1)^2+1]｝
=[(3-1)^2+1]/[(53+1)^2+1]｝
=5/2917