Which justification best explains why multiplying both sides of a rational equation by the LCD is a valid step when solving rational equations (provided you track restrictions)?

Multiplying by the LCD removes denominators by cancelation and yields an equivalent equation for values not excluded by denominators, but you must record excluded values first

Multiplying by the LCD is a shortcut that allows you to cancel numerators rather than denominators and therefore speeds up computation

Multiplying by the LCD always gives every solution to the equation without the need to check restrictions after solving

Multiplying by the LCD is only permitted if all denominators are linear and cannot be used otherwise