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let numbers are x, x+4
Now 1/x-1/x+4=4/21
Or, x+4-x/x(x+4)=4/21
Or, 4/x^2+4x=4/21
Or, 1/x^2+4x=1/21
Or,x^2+4x=21
Or, x^2+4x-21=0
Or, x^2+7x-3x-21=0
Or, x(x+7)-3(x+7)=0
Or, (x+7)(x-3)=0
Hence x+7=0
Or, x=-7
OR x-3=0
Or, x=3
hence the numbers are -7,-7+4=-3
Or 3,3+4=7
Now 1/x-1/x+4=4/21
Or, x+4-x/x(x+4)=4/21
Or, 4/x^2+4x=4/21
Or, 1/x^2+4x=1/21
Or,x^2+4x=21
Or, x^2+4x-21=0
Or, x^2+7x-3x-21=0
Or, x(x+7)-3(x+7)=0
Or, (x+7)(x-3)=0
Hence x+7=0
Or, x=-7
OR x-3=0
Or, x=3
hence the numbers are -7,-7+4=-3
Or 3,3+4=7
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