Let $X\subseteq\mathbb{C}P^n$ be s smooth variety. Let $C\subseteq X$ be an algebraic rational curve [i.e. an algebraic curve which is birational to $\mathbb{C}P^1$].

In what follows, we consider $H_2(X;\mathbb{Q})$.

I think that I was told that the following statement is true:

There exist rational numbers $r_1,\ldots,r_k$ and holomorphic curves $u_1,\ldots,u_k:\mathbb{C}P^1\longrightarrow X$ so that $$[C]=r_1(u_1)_*[\mathbb{C}P^1]+\ldots+r_k(u_k)_*[\mathbb{C}P^1].$$

Why?

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