Simplify:
(1)/(t^2+t)+(1)/(t^2-t)
To simplify the expression (1)/(t^2+t)+(1)/(t^2-t), we need to find a common denominator and combine the fractions.
Step 1: Find the common denominator.
The common denominator for the two fractions is (t^2+t)(t^2-t). This is because (t^2+t) and (t^2-t) are two different factors of the denominator.
Step 2: Rewrite the fractions with the common denominator.
Now, let's rewrite each fraction with the common denominator:
(1)/(t^2+t) = (1)(t^2-t)/(t^2+t)(t^2-t)
(1)/(t^2-t) = (1)(t^2+t)/(t^2+t)(t^2-t)
Step 3: Combine the fractions.
Now that we have the fractions with the same denominator, we can add them together:
[(t^2-t) + (t^2+t)] / [(t^2+t)(t^2-t)]
Step 4: Simplify the expression.
Combine the like terms in the numerator:
2t^2 / (t^2+t)(t^2-t)
Step 5: Factor out the common terms, if possible.
In this case, there are no common factors we can simplify. So, the expression remains as 2t^2 / (t^2+t)(t^2-t).
Therefore, the simplified expression is 2t^2 / (t^2+t)(t^2-t).