5s/(s^2-t^2) - s/(s-t)
using a common denominator, we have
5s/(s^2-t^2) - s(s+t)/(s^2-t^2)
(5s-s(s+t))/(s^2-t^2)
s(5-s-t)/(s^2-t^2)
thanks
To simplify the expression (5s/(s^2-t^2)) - (s/(s-t)), we will need to find a common denominator and then combine the terms.
Step 1: Factor the denominators
The denominator of the first term, s^2 - t^2, can be factored as (s+t)(s-t). The denominator of the second term, s - t, is already factored.
Step 2: Finding the common denominator
To find the common denominator, we take the product of both denominators, which gives us (s+t)(s-t)(s-t).
Step 3: Convert both fractions to have the common denominator
To convert the first fraction, 5s/(s^2-t^2), we multiply the numerator and denominator by (s-t), which results in:
(5s(s-t))/((s+t)(s-t)(s-t))
The second fraction, s/(s-t), already has the common denominator.
Step 4: Combining the terms
Now that both fractions have the common denominator, we can combine them. The expression becomes:
(5s(s-t))/((s+t)(s-t)(s-t)) - (s(s+t))/((s+t)(s-t)(s-t))
Step 5: Simplify the expression
To simplify further, we can simplify the common denominator and combine the numerators:
(5s(s-t) - s(s+t))/((s+t)(s-t)(s-t))
Step 6: Expand and group like terms in the numerator
Expanding the numerator gives us: (5s^2 - 5st - s^2 - st) / ((s+t)(s-t)(s-t))
Simplifying the numerator yields: 4s^2 - 6st / ((s+t)(s-t)(s-t))
Thus, the simplified expression is (4s^2 - 6st) / ((s+t)(s-t)(s-t))