Question

Help with this

Answer 1

The rational expression \[\frac{ x^{2} + 3x}{ 4x }\] is simplified to \[\frac{ x + 3 }{ 4 }\] . Explain why this new expression is not defined for all values of x.

Answer 2

assume that we are looking at a map while trying to drive down the road. which is more important .... the bridge being out in front of you, or the map saying to cross the bridge?

Answer 3

The bridge...

Answer 4

yeah, the first expression models some real life issue. the simplified version is a map that can make things simpler but it doesnt really negate the real life issues does it

Answer 5

x=0 is not a usable value in the real life issue. so regardless of how much we simplify it to make a map, x=0 is still not going to work for us

Answer 6

So the answer would be... "the expression is not defined for all values of x because x can not equal to 4" ?

Answer 7

... becuase x cannot be equal to 0. its simply not a part of the domain that we are simplifying with

Answer 8

Ah, because x is not there, it's gone, right? So there is nothing to equal x to?

So I would write "The new expression is not defined for all values of x because x is not part of the domain for the new expression. If there is no domain, it will remain not defined (undefined)."

Answer 9

\[\frac{x^2+3x}{4x}=\frac{x}{x}~\frac{x+3}{4}\]
now, x/x is defined for all x not equal to 0 since 0/0 is undefined

Answer 10

that sounds fair to me

Answer 11

So my response would be appropriate, yes?

Answer 12

appropriate enough for me yes, but im not the one to grade it

Answer 13

"... is not defined for all values of x because [0] is not part of the domain to start with ..."

Answer 14

\[\frac xx~\frac{x+3}{4}=\frac{x+3}{4};~x\ne0\]

Answer 15

Got it, thank you

Answer 16

good luck :)