Simplify the rational expression state any restrictions on the variable
t^2+2t-24 / t^2-36
I got t-4 / t-6, but Im not sure of the restrictions whether its 6 or -6,6
So the answer is t-4/t-6,t=/6
the answer choices only give =/6 or =/-6,6 so now confused
Well, well, well, we have a rational expression here! Let's see if I can help you out with your simplification.
The expression you got, t-4 / t-6, is partially correct. Good job on that! However, we need to find the restrictions on the variable t.
To do that, we look at the denominator: t^2-36. This expression can be factored as (t-6)(t+6). Ah, algebraic magic!
Now, here's the important part. The denominator cannot be equal to zero, which means we have these two restrictions:
1. t-6 ≠ 0
2. t+6 ≠ 0
From the first restriction we get t ≠ 6, and from the second restriction we get t ≠ -6.
So, the correct restrictions on the variable t are t ≠ 6 and t ≠ -6.
Keep up the good work with those rational expressions, my friend!
To simplify the rational expression (t^2 + 2t - 24) / (t^2 - 36), we can start by factoring both the numerator and denominator:
Numerator: t^2 + 2t - 24
Factor the numerator by finding two numbers that multiply to -24 and add up to +2. The numbers are +6 and -4.
So, t^2 + 2t - 24 = (t + 6)(t - 4)
Denominator: t^2 - 36
The denominator is a difference of squares, so we can factor it as (t + 6)(t - 6).
Now, we can simplify the rational expression:
(t^2 + 2t - 24) / (t^2 - 36) = (t + 6)(t - 4) / (t + 6)(t - 6)
Here, we can see that the (t + 6) terms in the numerator and denominator cancel each other out, leaving us with:
(t - 4) / (t - 6)
So, the simplified form of the rational expression is (t - 4) / (t - 6).
Now, let's determine the restrictions on the variable. Restrictions occur when the denominator becomes zero because division by zero is undefined.
In this case, the denominator is (t - 6), so the restriction is t ≠ 6.
Therefore, the restrictions on the variable t are t ≠ 6.