document.write( "Question 718682: Simplify the rational expression. State any restrictions on the variable.
\n" ); document.write( "Much appreciated!!\r
\n" ); document.write( "\n" ); document.write( "t2+2t-24/t2-36 \n" ); document.write( "
Algebra.Com's Answer #441003 by jsmallt9(3758)\"\" \"About 
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:
\n" ); document.write( "\"t%5E2%2B2t-24%2Ft%5E2-36\"
\n" ); document.write( "But I suspect what you intended was:
\n" ); document.write( "\"%28t%5E2%2B2t-24%29%2F%28t%5E2-36%29\"
\n" ); document.write( "Unclear problems are less likely to get a response. So it is to your advantage to take the time to post correctly.

\n" ); document.write( "\"%28t%5E2%2B2t-24%29%2F%28t%5E2-36%29\"
\n" ); document.write( "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:
\n" ); document.write( "\"%28%28t%2B6%29%28t-4%29%29%2F%28%28t%2B6%29%28t-6%29%29\"

\n" ); document.write( "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:
\n" ); document.write( "(t+6)(t-6) = 0
\n" ); document.write( "and solve. (We could have used the original denominator, \"t%5E2-6+=+0\", but we would have factored that to solve it anyway.) Using the Zero Product Property:
\n" ); document.write( "t+6 = 0 or t-6 = 0
\n" ); document.write( "Then solve these. (I'll leave that up to you to finish.) Remember, these are values we must not allow t to have!

\n" ); document.write( "Now we can simplify. Looking at:
\n" ); document.write( "\"%28%28t%2B6%29%28t-4%29%29%2F%28%28t%2B6%29%28t-6%29%29\"
\n" ); document.write( "we can see that there are factors we can cancel:
\n" ); document.write( "\"%28cross%28%28t%2B6%29%29%28t-4%29%29%2F%28cross%28%28t%2B6%29%29%28t-6%29%29\"
\n" ); document.write( "leaving:
\n" ); document.write( "\"%28t-4%29%2F%28t-6%29\"
\n" ); document.write( "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.) \n" ); document.write( "
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