How Do You Simplify Complex Algebraic Fractions?

[Jason-Li]

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

 

[PeroK]

In general $$\frac 1 a + \frac 1 b + c = \frac{b + a + abc}{ab}$$
So, the book is correct.

I think you are confusing $10^{-5}$ with $\frac 1 {10^5}$ in terms of how you treat it as a fraction.

 

[PeroK]

PS you can always set $n = 1$ and put each expression into a calculator or spreadsheet. You'll see that your expression is incorrect.

 

[Jason-Li]

In general $$\frac 1 a + \frac 1 b + c = \frac{b + a + abc}{ab}$$
So, the book is correct.

I think you are confusing $10^{-5}$ with $\frac 1 {10^5}$ in terms of how you treat it as a fraction.

PeroK,

I should've simplified it down first like you have e.g. abc...

Thanks again!

 

[FactChecker]

I think you are confusing $10^{-5}$ with $\frac 1 {10^5}$ in terms of how you treat it as a fraction.

That would be fine, since they are equal, as long as it was done correctly.

 

[Mark44]

So my final equation is: $\frac {1} {2700} + \frac {1} {3930n^2} + 10^{-5}$

Nit: That's not an equation. An equation is a statement about the equality of two expressions. An equation will always include at least one = symbol.

 

[WWGD]

Nit: That's not an equation. An equation is a statement about the equality of two expressions. An equation will always include at least one = symbol.

And a good way of remembering is looking at the first 4 letters of the word : Edit :equa(l)(ity)

 

[Mark44]

And a good way of remembering is lo9king at the first 4 letters of the word : aqua(l)(ity)

aqua?

 

[WWGD]

aqua?

Auto (in)correct strikes again. Let me edit.