# Thread: Complicated Fractions

1. ## Complicated Fractions

Hi there, I am new to the forums so I hope I am posting this in the right spot. I am studying Physics but seem to be hitting a roadblock when doing some more complicated fractions. I am sure that once I see it I will understand but would appreciate any help! I will list the two problems I am working on, thanks!

Problem 1:

Trying to solve for $\displaystyle F_{f}$!

$\displaystyle \frac {1}{P} = \frac {F_{f}}{P_{f}} + \frac {1 - F_{f}}{P_{L}}$

Problem 2:

Trying to reduce!

$\displaystyle mgsin\Theta - \frac {mgsin\Theta}{1 + \frac {I_{c}}{MR^2}} = 0$

2. Originally Posted by Raezputin
Hi there, I am new to the forums so I hope I am posting this in the right spot. I am studying Physics but seem to be hitting a roadblock when doing some more complicated fractions. I am sure that once I see it I will understand but would appreciate any help! I will list the two problems I am working on, thanks!

Problem 1:

Trying to solve for $\displaystyle F_{f}$!

$\displaystyle \frac {1}{P} = \frac {F_{f}}{P_{f}} + \frac {1 - F_{f}}{P_{L}}$

Problem 2:

Trying to reduce!

$\displaystyle mgsin\Theta - \frac {mgsin\Theta}{1 + \frac {I_{c}}{MR^2}} = 0$
$\displaystyle \frac {1}{P} = \frac {F_{f}}{P_{f}} + \frac {1 - F_{f}}{P_{L}}$

Note that $\displaystyle \frac{1-F_f}{P_L} = \frac{1}{P_L} - \frac{F_f}{P_L}$

Subtract $\displaystyle \frac{1}{P_L}$ to both sides and get the same denominator:

$\displaystyle \frac{1}{P} - \frac{1}{P_L} = \frac{P-P_L}{PP_L}$

On the rhs:$\displaystyle \frac{F_f}{P_f} - \frac{F_f}{P_L} = \frac{F_fP_L - F_fP_f}{P_fP_L}$

Overall: $\displaystyle \frac{P-P_L}{PP_L} = \frac{F_fP_L - F_fP_f}{P_fP_L}$

Factor $\displaystyle F_f$ and solve relatively easily

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2. $\displaystyle mgsin\Theta - \frac {mgsin\Theta}{1 + \frac {I_{c}}{MR^2}} = 0$

Let $\displaystyle \alpha = \frac {I_{c}}{MR^2}$ so that

$\displaystyle mgsin\Theta - \frac {mgsin\Theta}{1 + \frac {I_{c}}{MR^2}} = 0$ becomes $\displaystyle mgsin\Theta - \frac {mgsin\Theta}{1 + \alpha} = 0$

Multiply through by $\displaystyle 1+\alpha$

$\displaystyle mgsin\Theta + \alpha mgsin\Theta - mgsin\Theta =0$

Cancelling: $\displaystyle \alpha mgsin\Theta = 0$ $\displaystyle = \frac {I_{c}}{MR^2}mgsin\Theta=0$

3. Hey e^ thanks for the quick response, only had time to go through the first problem but had a question.

You said:

$\displaystyle \frac{1}{P} - \frac{1}{P_L} = \frac{P-P_L}{PP_L}$

But with the cross multiplication on the left shouldnt it be

$\displaystyle \frac{1}{P} - \frac{1}{P_L} = \frac{P_L-P}{PP_L}$

The numbers came out correct but had a negative up top which made me look again. Also, after the switch I get the correct answer but the book gives me this as a solution:

$\displaystyle F_F = \frac{1-\frac{P_L}{P}}{1-\frac{P_L}{P_F}}$

Now it doesnt really matter, cause when I run the math I get the same answer, just wondering cause im curious =)

Thanks for the help!

4. Question 2:

Hehe forgot to state that it was equal to a variable that was needed, instead of 0. But the tips you gave me still allowed me to solve on my own! Thanks again e^

-Raez