could someone help with rationals?

Question

Indicate any restrictions on the variable in the following rational expression, then reduce the rational expression to lowest terms.
If it is already in lowest terms, enter the expression in the answer box.

 

a+2/(a²-4)

 

and i got 1/(a-2)

 

but then the next question asks: Variable restrictions on the original expresssion: a≠ _____ x _____

Answer 1

The denominator of a fraction may not be 0. Any value of the variable that makes the denominator 0 is not allowed.

In the given fraction, if a = 2, the denominator is 0. Therefore a ∉ {2}.

Answer 2

Hi Jared.

 

From the second part of your post, it seems your original expression is

 

(a+2)/(a²-4)

Parentheses make it so much easier to understand.

 

I agree that this expression would simplify to 1/(a-2)

 

But recall the original denominator was a²-4.  

This can be factored as (a+2)(a-2)

Setting this equal to 0 and solving for a, we have

a= 2 or -2

 

 

If a = 2 or a = -2 then the denominator would equal 0.

If this is the case the expression is undefined, since you can't divide by 0.

 

So the restriction son the original expression are a≠2, -2