(s*(C/CF+1)+1/(RF*CF))/(s*(C+1)+(1/(RF*CF)))

asked by guest
on Jan 12, 2025 at 11:07 am



You asked:

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

MathBot Answer:

Evaluated



\(\displaystyle \frac{s \left(\frac{C}{C F} + 1\right) + \frac{1}{R F C F}}{s \left(C + 1\right) + \frac{1}{R F C F}} = \frac{s \left(1 + \frac{1}{F}\right) + \frac{1}{F^{2} C R}}{s \left(C + 1\right) + \frac{1}{F^{2} C R}} \)

Expanded

\[\frac{s \left(\frac{C}{C F} + 1\right) + \frac{1}{R F C F}}{s \left(C + 1\right) + \frac{1}{R F C F}} = \frac{s}{C F s + F s + \frac{1}{C F R}} + \frac{s}{C s + s + \frac{1}{F^{2} C R}} + \frac{1}{C^{2} F^{2} R s + F^{2} C R s + 1}\]

Factored

\[\frac{s \left(\frac{C}{C F} + 1\right) + \frac{1}{R F C F}}{s \left(C + 1\right) + \frac{1}{R F C F}} = \frac{F^{2} C R s + C F R s + 1}{C^{2} F^{2} R s + F^{2} C R s + 1}\]

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