Simplifying an expression
- Thread starter Howard
- Start date
Just doing it in my head, I don't think you can...
common denominator in the bottom fraction yields
r(r+5.6)(r+10)+100*kr
-------------------------------------
r(r+5.6)(r+10)
in the bottom half of the expression. Then cancel the r(r+5.6)(r+10) from bottom of both the numerator and denominator of the big fraction to get
100
------------------------------------
r(r+5.6)(r+10)+100*kr
Unless I'm doing something stupid... You can't go from this to that.
common denominator in the bottom fraction yields
r(r+5.6)(r+10)+100*kr
-------------------------------------
r(r+5.6)(r+10)
in the bottom half of the expression. Then cancel the r(r+5.6)(r+10) from bottom of both the numerator and denominator of the big fraction to get
100
------------------------------------
r(r+5.6)(r+10)+100*kr
Unless I'm doing something stupid... You can't go from this to that.
Well, if you try to plug in numbers, you'll quickly come to the conclusion that your professor may have erred in his solution.
Just multiply the whole expression by r(r+5.6)(r+10) / r(r+5.6)(r+10) == 1. Then, things just cancel out like magic.
Oh, out of curiosity, what college course is this?
The bottom half of your big fraction is:
1+100/(r(r+5.6)(r+10))*(kr)
Which can be rewritten
1+100kr/(r(r+5.6)(r+10))
To add these fractions, multiply the 1 by (r(r+5.6)(r+10))/(r(r+5.6)(r+10))
r(r+5.6)(r+10)/(r(r+5.6)(r+10))+100kr/(r(r+5.6)(r+10))
Now you have common denominator in the fractions, so you can add them:
r(r+5.6)(r+10)+100kr
----------------------------------------
r(r+5.6)(r+10)
This is the bottom of the big fraction. Now the whole expression is a big fraction with a fraction on top & a fraction on bottom. To divide them, multiply by the reciprocal (that's top fraction * bottom fraction flipped over). The r(r+5.6)(r+10) cancels and you're left with what I wrote at the end.
Sorry if I'm going into too much/too little detail. It's dangerously easy to offend people by going either way...
This looks like it came out of the transformed equations for a feedback control problem. In fact given the (100/blah)/(1+100kr/blah) format I'm almost certain it is, lol.
Almost -always-, the first thing you should do is clear out the 'blah'. You usually have an equation in the form of: (A/f(r))/(1 + k(r)*A/f(r)). Imagine if the equation were (A/f(r))/(k(r)*A/f(r))... that's obviously 1/k(r) right? And you can get there by multiplying through by f(r)/f(r). With the feedback equation, multiplying through by f(r)/f(r) achieves a similar effect... now you're left with: A/(f(r) + k(r)*A) which is simply A/polynomial. And the form A/polynomial is a well-understood, well-documented system that you can relatively easily analyze. A/polynomial is just about always your goal.
Almost -always-, the first thing you should do is clear out the 'blah'. You usually have an equation in the form of: (A/f(r))/(1 + k(r)*A/f(r)). Imagine if the equation were (A/f(r))/(k(r)*A/f(r))... that's obviously 1/k(r) right? And you can get there by multiplying through by f(r)/f(r). With the feedback equation, multiplying through by f(r)/f(r) achieves a similar effect... now you're left with: A/(f(r) + k(r)*A) which is simply A/polynomial. And the form A/polynomial is a well-understood, well-documented system that you can relatively easily analyze. A/polynomial is just about always your goal.
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