When solving a rational equation?

Question

why is it OK to remove the denominator by
multiplying both sides by the LCD and why can you not do the same operation
when simplify a rational expression.

Answer 1

You can multiply an equation by a constant (LCD, for instance) without changing the sense of an expression. For instance, if you say 2apples = 20p and 4 apples =40p you are saying the same thing. You are multiplying the left and right hand side of the equation by a constant without changing the sense of the equation. When you multiply both sides of a rational equation by the LCD you are doing the same thing.

When simplifying a rational expression you cannot do this because you are changing the value of your answer. For instance, if you owe someone 5/2 sterling, say, i.e. 2.5 sterling, you wouldn't multiply your answer by 2 to remove the denominator, because you'll end up owing 5 sterling instead.

So an equation can be multiplied by a constant but a single term cannot.

Answer 2

An expression is different from an equation in that it is not set equal to anything.

The expression x/3 +x/4
= 4x/12+ 3x/12
= 7x/12 and that's as far as you can go.

But if we have the equation x/3 +x/4 = 1
we have 4x/12 +3x/12 = 12/12
7x/12 =12/12
Since denominators are equal the numerators must be =
Hence 7x =12 and x = 12/7