## Pool Shares In this lesson, we will derive an equation to calculate how many pool shares we need to mint when we add liquidity to a Uniswap V2 pool. We will use the following variables: * **S = shares to mint** * **T = total shares** * **L1 = liquidity after adding liquidity** * **L0 = liquidity before adding liquidity** We know that the ratio of tokens we provide when adding liquidity (dY / dX) must equal the spot price. This relationship can be expressed as: ``` L1 - L0 / L0 = dX / X0 = dY / Y0 ``` This equation indicates that the change in liquidity (L1 - L0) relative to the initial liquidity (L0) is equivalent to the amount of token X (dX) we provide divided by the initial amount of token X (X0). Similarly, it's equal to the amount of token Y (dY) we provide divided by the initial amount of token Y (Y0). Using this information, we can derive the following equation for the number of shares to mint: ``` S = (L1 - L0 / L0) * T ``` This equation tells us the number of shares (S) we need to mint based on the change in liquidity (L1 - L0), the initial liquidity (L0), and the total number of shares (T). We will explore this equation in more detail in future lessons.