SOLUTION: Simplify the rational expression. State any restrictions on the variable. Much appreciated!! t2+2t-24/t2-36

Question 718682: Simplify the rational expression. State any restrictions on the variable.
Much appreciated!!
t2+2t-24/t2-36
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
First of all, please use the "^" character to indicate exponents (just like on a calculator) and put numerators and denominators in parentheses. Assuming t2 means t^2, what you posted meant:

But I suspect what you intended was:

Unclear problems are less likely to get a response. So it is to your advantage to take the time to post correctly.

To do both parts of this problem, simplify and find restrictions, we need to see the fraction with numerator and denominator in factored form. Factoring we get:

Any time you have a variable in a denominator, you must make sure that the variable never has a value that would turn that denominator into a zero (since we may never divide by zero!). Our denominator is (t+6)(t-6). Perhaps you can already see what values for t that would make this denominator zero. If not, then set the denominator to zero:
(t+6)(t-6) = 0
and solve. (We could have used the original denominator, , but we would have factored that to solve it anyway.) Using the Zero Product Property:
t+6 = 0 or t-6 = 0
Then solve these. (I'll leave that up to you to finish.) Remember, these are values we must not allow t to have!

Now we can simplify. Looking at:

we can see that there are factors we can cancel:

leaving:

This is the simplified fraction. (Note: The t's here do not cancel! Only factors may be canceled and neither of those t's are factors of the numerator or denominator.)
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