# abstract algebra: a problem related to polynomial rings and ideals

I need to demonstrate the following result, but I don't know how to proceed:

Leave $$k (X)$$ be a polynomial ring and leave $$I, J$$ be ideal of $$k (X)$$. In the ring $$k (X, t)$$ ($$t$$ it is a new indeterminate) is considered the ideal $$L = tI + (1-t) J$$. Test it $$I cap J = L cap k (X)$$.

I would be really grateful if you could help me.