SOLUTION: When solving a rational equation, why it is OK to remove the denominator by multiplying both sides by the LCD and why can you not do the same operation when simplifying a rational

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Question 15188: When solving a rational equation, why it is OK to remove the denominator by multiplying both sides by the LCD and why can you not do the same operation when simplifying a rational expression or adding rational expressions?
The only answere that I have come up with so far is the one is an expression and one is an equation. With the equation we are solving for a variable, and with an expression we are simplyfying and then doing what is required ie, add, subtract, multiple or divide. Is there more to this question that I am missing?

Answer by rapaljer(4551) About Me  (Show Source):
You can put this solution on YOUR website!
This is one of my favorite questions, and I answer it every day! If you have an EQUATION, then the multiplication property of equations allows you to multiply BOTH SIDES of an EQUATION by the same NON-ZERO number. However, if you have a rational EXPRESSION, then you do NOT have an equation, so the properties of EQUATIONS do NOT apply! Moreover, you can't solve an expression. About all you can do with expressions is add, subtract, multiply, divide, simplify or factor them.

R^2 at SCC