Simplify expression

Question

I am doing a question and know the answer but don't understand the simplifying part

 

1/(1+(1/t)^2) * (1/t^2)

 

The answer is 

 

1/(t^2+1)    but I don't understand how to simplify the above expression

Answer 1

Hi, Ian, 

 

So what you are doing is multiplying fractions. When multiplying fractions, you have to multiply across. First multiply the numerators together, then multiply the denominators. In this case, the numerators for both fractions are 1, so 1*1 = 1. The denominators in this problem are [1+(1/t)²]and t². Also, you must know that (1/t)² is the same thing as 1/t². To multiply the denominators, you need to distribute t² to 1+ 1/t². So you have to do t^2*1 + t^2*(1/t^2). Remember, just like 3*(1/3) = 3/3 = 1, the same is true for t^2 * (1/t^2)--it also equals 1. Here is the work below:

 

(1/t² )*[1/(1+1/t²)]=(1*1)/(t²*(1+1/t²) )=1/(t²*1+t²*1/t²)=1/(t²+t²/t² )=1/(t²+1)

 

I hope this helps :)

 

Emmanuel