t^2/�ã(t^2+1) - �ã(t^2+1)
-------------------------
t^2
Is the final answer -1/t^2 sqrt(t^2+1)
The a is supposed to be a square root
you have
t^2/√(t^2+1) - √(t^2+1)
----------------------------
t^2
Combine the terms in the numerator and denominator
t^2 - (t^2+1)
---------------------
t^2 √(t^2+1)
-1/(t^2 √(t^2+1))
To find the value of the given expression, let's simplify step by step:
Step 1: Simplify the numerator
The numerator of the expression is:
t^2/�ã(t^2+1) - �ã(t^2+1)
To simplify this, we need to rationalize the denominators of the two terms:
�ã(t^2+1) can be rationalized by multiplying the expression by its conjugate, which is �ã(t^2+1).
So, the numerator becomes:
[t^2 * �ã(t^2+1) - �ã(t^2+1) * �ã(t^2+1)]
Expanding the numerator, we get:
[t^2 * �ã(t^2+1) - (t^2+1)]
Simplifying further, we have:
t^2*�ã(t^2+1) - t^2 - 1
Step 2: Simplify the denominator
The denominator of the expression is t^2.
Step 3: Combine the numerator and denominator
The final expression becomes:
[t^2 * �ã(t^2+1) - t^2 - 1] / t^2
Now, let's simplify this expression further:
First, simplify the numerator:
t^2 * �ã(t^2+1) - t^2 - 1
Taking out the common factor of t^2, we can rewrite it as:
t^2 * [�ã(t^2+1) - 1] - 1
Next, let's simplify the expression inside the square root:
�ã(t^2+1) - 1 can be expanded as:
�ã(t^2+1) - �ã(1)
Expanding further, we get:
�ã(t^2+1) - �ã(1) = �ã(t^2+1) - 1
Substituting this back into the numerator, we have:
t^2 * [�ã(t^2+1) - 1] - 1 = t^2 * �ã(t^2+1) - t^2 - 1
Finally, after simplifying the numerator and denominator, the expression is:
[t^2 * �ã(t^2+1) - t^2 - 1] / t^2
Therefore, the final answer is not -1/t^2 * sqrt(t^2+1).