- #1

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- Homework Statement
- Working through some fractions in loop-gain of an oscillator and stuck when comparing my answer to the learning materials...

- Relevant Equations
- algebra & fractions

So my final equation is:

##\frac {1} {2700} + \frac {1} {3930n^2} + 10^{-5}##

I need to boil this down, the learning materials has the following working, but I can't seem to get it

$$\frac {1} {2700} + \frac {1} {3930n^2} + 10^{-5}$$

$$\frac {3930n^2+2700+2700*3930n^2*10^{-5}} {(2700*3930n^2)}$$

But I have the following:

$$\frac {(3930n^2+2700)*10^{-5}+2700*3930n^2*10^{-5}} {(2700*3930n^2)}$$

Not sure why I have the extra 10^{-5} or how to get rid of it?

Unless the following makes mathematical sense? by making 10^{-5} = 1/ 10^{5}

$$\frac {(3930n^2+2700)*10^{5}+2700*3930n^2} {(2700*3930n^2)*10^5}$$

$$\frac {(3930n^2+2700)+2700*3930n^2*10^{-5}} {(2700*3930n^2)}$$

But the problem is $$\frac {(3930n^2+2700)*10^{5}+2700*3930n^2} {(2700*3930n^2)*10^5} ≠ \frac {(3930n^2+2700)+2700*3930n^2*10^{-5}} {(2700*3930n^2)}$$

##\frac {1} {2700} + \frac {1} {3930n^2} + 10^{-5}##

I need to boil this down, the learning materials has the following working, but I can't seem to get it

$$\frac {1} {2700} + \frac {1} {3930n^2} + 10^{-5}$$

$$\frac {3930n^2+2700+2700*3930n^2*10^{-5}} {(2700*3930n^2)}$$

But I have the following:

$$\frac {(3930n^2+2700)*10^{-5}+2700*3930n^2*10^{-5}} {(2700*3930n^2)}$$

Not sure why I have the extra 10^{-5} or how to get rid of it?

Unless the following makes mathematical sense? by making 10^{-5} = 1/ 10^{5}

$$\frac {(3930n^2+2700)*10^{5}+2700*3930n^2} {(2700*3930n^2)*10^5}$$

$$\frac {(3930n^2+2700)+2700*3930n^2*10^{-5}} {(2700*3930n^2)}$$

But the problem is $$\frac {(3930n^2+2700)*10^{5}+2700*3930n^2} {(2700*3930n^2)*10^5} ≠ \frac {(3930n^2+2700)+2700*3930n^2*10^{-5}} {(2700*3930n^2)}$$

Last edited: