group homomorphism

Hello.

I'm trying to determine the kernel of the following group
homomorphism:

k[X/Y,Z/Y]/f_1 + k[X/Z,Y/Z]/f_2 -> k[X/Y,Z/Y,Y/Z]/f_1,

where k is a (alg. closed) field and F is is a given homogeneous
polynomial in variables X, Y, Z of degree d
and f_1(X/Y,Z/Y) = F(X/Y,1,Z/Y) and f_2(X/Z,Y/Z) = F(X/Z,Y/Z,1).

This is a problem in section 2 of chapter 3 of hartshorne. The answer
seems to be k.

Thanks,
N.

.

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