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WHY rational expressions that are being added must have an LCD, but rational expressions that are being multiplied do not need to have an LCD.

The short answer is that addition and multiplication are different operations with different properties.
If we added rational expressions directly without using the LCD the answer would be nonsense. Consider this
1/2 + 1/2 = (1+1)/(2+2) = 2/4 = 1/2 ??
Does that make any sense?
We know the right answer should be 1/2 + 1/2 = 1.

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