Perform the indicated operation and simplify if possible. Assume any factors you cancel are not zero.
s/(s^2-5s-24)-4/(s+3)
factor it first
s/(s^2-5s-24)-4/(s+3)
= s/( (s-8)(s+3)) - 4(s+3) , LCD = (s-8)(s+3)
= ( s - 4(s-8) )/((s-8)(s+3))
= (32 - 3s)/((s-8)(s+3))
or
= - (3s-32)/((s-8)(s+3))
To perform the indicated operation and simplify the expression, we need to find a common denominator for the two fractions. The denominators in this case are (s^2 - 5s - 24) and (s + 3).
First, let's factor the denominator of the first fraction, s^2 - 5s - 24:
s^2 - 5s - 24 = (s - 8)(s + 3)
Now, the common denominator for the two fractions is (s - 8)(s + 3).
To convert the first fraction to the common denominator, we need to multiply its numerator and denominator by (s + 3):
s/(s^2 - 5s - 24) = s/(s - 8)(s + 3) * (s + 3)/(s + 3) = s(s + 3)/[(s - 8)(s + 3)]
Now, let's simplify the second fraction -4/(s + 3):
We don't need to do anything to this fraction since the denominator is already (s + 3).
Now, we can rewrite the expression with a common denominator:
[s(s + 3)/[(s - 8)(s + 3)] - 4/(s + 3)]
Next, we can combine the fractions by subtracting them:
[s(s + 3) - 4]/[(s - 8)(s + 3)]
Now, let's expand and simplify the numerator:
[s^2 + 3s - 4]/[(s - 8)(s + 3)]
This expression is the simplified form of the given operation.