(s*(C/A+1)+1/(B*A))/(s*(C+1)+(1/(A*B)))

asked by guest
on Jan 12, 2025 at 11:08 am



You asked:

Evaluate the expression: \(\frac{s \left(\frac{C}{A} + 1\right) + \frac{1}{B A}}{s \left(C + 1\right) + \frac{1}{A B}}\)

MathBot Answer:

Evaluated



\(\displaystyle \frac{s \left(\frac{C}{A} + 1\right) + \frac{1}{B A}}{s \left(C + 1\right) + \frac{1}{A B}} = \frac{s \left(1 + \frac{C}{A}\right) + \frac{1}{A B}}{s \left(C + 1\right) + \frac{1}{A B}} \)

Expanded

\[\frac{s \left(\frac{C}{A} + 1\right) + \frac{1}{B A}}{s \left(C + 1\right) + \frac{1}{A B}} = \frac{C s}{A C s + A s + \frac{1}{B}} + \frac{s}{C s + s + \frac{1}{A B}} + \frac{1}{A B C s + A B s + 1}\]

Factored

\[\frac{s \left(\frac{C}{A} + 1\right) + \frac{1}{B A}}{s \left(C + 1\right) + \frac{1}{A B}} = \frac{A B s + B C s + 1}{A B C s + A B s + 1}\]

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