Are a rational expression and its simplified forms equivalent? Provide mathematical examples to support your opinions.

Somebody please explain!

Question

Are a rational expression and its simplified forms equivalent? Provide mathematical examples to support your opinions.

Somebody please explain!

deoxna · Answer

Just use an example you know is true:

$$\frac{ 4 }{ 8 } x = \frac{ 1 }{ 2 } x $$

Multiply both sides by two and you get

x=x

deoxna · Answer

You could forget the x part is you think of x=1, but it will work for any x.

anonymous · Answer

Hmm.. okay that seems more simple than I thought, thanks!

deoxna · Answer

Anytime :)

anonymous · Answer

wait wait wai.. Isn't a rational expression a ratio of two polynomials?

anonymous · Answer

Wouldn't it have to be something like (x^2 +5)/(x+2)?

anonymous · Answer

No... rational means it can be expressed as a fraction with integers on top and bottom

deoxna · Answer

Both a ratio of polynomials and of integers are a "rational expression", and, in any case, you can use the same example to prove it for polynomials as well.

anonymous · Answer

Oh, okay thanks! :)

anonymous · Answer

What about ((x^2)+10)/(x+5)=x+2?

anonymous · Answer

x+2 is the reduced form, but it doesn't turn out to x=x does it?