Solving for x: Are F(x) and G(x) Equivalent?

[brycenrg]

F(x) = (x^2 - x)/(x-1)
G(x)= x

I factored x^2-x and canceled denominator of f(x) which simplify to x

So it does equal x does not now matter that in original equation x cannot = 1 otherwise denominator = 0

I'm just making sure they are = and but maybe not equivalent. Trying to learn more of maths. Thank you.

 

[ehild]

Is F(x) defined when x=1? Is G(x) defined there?

ehild

 

[brycenrg]

The problem doesn't say

 

[ehild]

Can you divide by zero? ehild

 

[brycenrg]

No but you can manipulate the equation to be x.

 

[ehild]

You manipulated it by dividing with an expression that can be zero. It is forbidden.
Try to input (1^2-1)/(1-1) in your calculator . What does it say?


ehild

 

[Mark44]

Do F and G have the same domains?

 

[haruspex]

The problem doesn't say

If it doesn't state the domains then, strictly speaking, it is impossible to say whether the functions are equal. I can claim the functions f = x and g = 2x are equal if the domain is {0}. Conversely, f = x and g = x are different functions if I specify different domains.

If no value is specified for F(1), is 1 in F's domain?
Consider whether 1 might be in G's domain, and the consequences.

 

[Mark44]

The problem doesn't say

It might be that the domains are implied - that is, the domain for each function might be the real numbers for which each function is defined. It might be that this is actually stated in the problem and you didn't include it in the problem description.

If there actually isn't any information given in the problem, what would be the implied domains for F and G?