maths question quick help needed

if you simplify an algebraic fraction that there is a binomial = numerator
polynomial = denominator

Now i saw a q, it asked for x values that are not valid.

So if an algebraic fraction not valid, it means it doesn't work so 1/0 values

Now, its simple ( ) ( ) ( ) poly factors,

well the simplfied version has ( ) ( ) meaning one factor cancelled.

Therefore to answer the x values invalidity, i do not refer to the simplified value, as it did not contain the other x value? I gave 2 x values from simplfiied fraction - i was looking there

Reply 1

mqb2766

Can you post the original question / example?

Original post by Batman2k1

Reply 2

Batman2k1

ok i used the simplified eq part

Original post by mqb2766

Can you post the original question / example?

Reply 3

mqb2766

A touch larger (less blurred) and pls explain your question?

Original post by Batman2k1

ok i used the simplified eq part

Reply 4

Batman2k1

Ok the question asks, what x values are invalid from this expression?
go 2 the link below.
I am saying i got 2 x values. Mark scheme has 3. Which is obvious because x-2 so x = 2 as 1/0 is invalid doesnt work.
I use the simplified expression. So as i got 2. I was wondering wait, i tried x=2 that expression, it still works, but i guess i meant 2 use the non simplfied exp?

https://imgur.com/a/lZU6V0K

Original post by mqb2766

A touch larger (less blurred) and pls explain your question?

Reply 5

mqb2766

Yes, when you cancel a factor like (x-2), you should specifically exclude x=2 from any further analysis. So there are 3 invalid values.

Original post by Batman2k1

Reply 6

Batman2k1

exclude x=2? Wouldn't you mean include? So do you suggest going back to the main form of the equation. See why does that happen? why cant i get x=2 from the simpl eq? - thanks

Original post by mqb2766

Yes, when you cancel a factor like (x-2), you should specifically exclude x=2 from any further analysis. So there are 3 invalid values.

Reply 7

mqb2766

When you cancel a term like (x-2) on the denominator, if x=2 you're effectively doing 0/0. So the resulting fraction (with cancelled terms) is not valid when x=2.

Original post by Batman2k1

exclude x=2? Wouldn't you mean include? So do you suggest going back to the main form of the equation. See why does that happen? why cant i get x=2 from the simpl eq? - thanks

Reply 8

Batman2k1

yes i know that looking back at the main equation with all the factors in. im saying, when answering invalidity q's do i not go to the resulting fraction - or s there some way i can work it out?
But if u do x=2 on the resulting fraction u get 6/5?
x=2 doesnt exist anymore? - hmm?

Original post by mqb2766

When you cancel a term like (x-2) on the denominator, if x=2 you're effectively doing 0/0. So the resulting fraction (with cancelled terms) is not valid when x=2.

Reply 9

mqb2766

For the invalid values, either
* list all the roots of the original denominator
* list all the roots of the simplified denominator + the cancelled roots
Same thing.

Original post by Batman2k1

Reply 10

mqb2766

For info
https://www.purplemath.com/modules/rtnldefs2.htm

Original post by Batman2k1

Reply 11

Batman2k1

Ohhhhh, so its a rule sort of. Okay, thanks, i will check the link now! question is a bit sneaky, never specifies which fraction to go to, but now i know now

Original post by mqb2766

For the invalid values, either
* list all the roots of the original denominator
* list all the roots of the simplified denominator + the cancelled roots
Same thing.

(edited 4 years ago)