Fraction Equations With Powers

**Shrinkwrap** · October 24th 2008, 06:38 PM

Hey, I hate to ask this much of someone to help but im in a real bad spot right now and my college exam is coming up monday and when handed a review to study, my mind went completely blank on half the review so I hope it wont be too much to ask if I request 5 or 6 problems that would help me the most.

The first one is, Subtract and simplify:

$ \frac {2x-3}{x+5} - \frac {x^2-4x-19}{x^2+8x+15} $

- I know you find the lowest common denominator but even after it still doesnt come out to correct answer. Like the $x^2-4x-19$ , but I couldnt find anything that can multiply other than 1 and -19 but still does not make 4.

Next one is simplifying it:

$ \frac {1 - \frac {3}{x} - \frac {10}{x^2}} {1 + \frac {11}{x} - \frac {18}{x^2}} $

- On this one I have no clue where to even start other than to possibly flip all 3 fractions on the second part to multiply but then I recall something about crossing like denominators out first but I dont know for sure.

This next one just says solve, it looks easy but...

$ 3x= \frac {4}{x} - \frac {13}{2} $

- I thought this would be an easy one but I am doing it wrong. It looked like a zero property one where you get everything to equal 0 but I have to get two answers and I am only getting one.

I actually think I said 5 or 6 equations but I dont want to ask too much of someone. If I can understand out how to do these ones on here it would help me better familiarize myself with the type of equations for the test coming. I may have trouble with a few more tomorrow so I may post a couple more here if its not gonna be too much to ask.

Thanks

**Chris L T521** · October 24th 2008, 06:53 PM

Originally Posted by Shrinkwrap

Hey, I hate to ask this much of someone to help but im in a real bad spot right now and my college exam is coming up monday and when handed a review to study, my mind went completely blank on half the review so I hope it wont be too much to ask if I request 5 or 6 problems that would help me the most.

The first one is, Subtract and simplify:

$ \frac {2x-3}{x+5} - \frac {x^2-4x-19}{x^2+8x+15} $

- I know you find the lowest common denominator but even after it still doesnt come out to correct answer. Like the $x^2-4x-19$ , but I couldnt find anything that can multiply other than 1 and -19 but still does not make 4.

Note that the denominator of the last term can be factored:

$x^2+8x+15=(x+3)(x+5)$

Now what do you think the LCD is?

Next one is simplifying it:

$ \frac {1 - \frac {3}{x} - \frac {10}{x^2}} {1 + \frac {11}{x} - \frac {18}{x^2}} $

- On this one I have no clue where to even start other than to possibly flip all 3 fractions on the second part to multiply but then I recall something about crossing like denominators out first but I dont know for sure.

Hint: $\frac{1 - \displaystyle\frac {3}{x} - \displaystyle\frac {10}{x^2}}{1 + \displaystyle\frac {11}{x} - \displaystyle\frac {18}{x^2}}=\frac{1 - \displaystyle\frac {3}{x} - \displaystyle\frac {10}{x^2}}{1 + \displaystyle\frac {11}{x} - \displaystyle\frac {18}{x^2}}\cdot\frac{{\color{red}x^2}}{{\color{red }x^2}}=\frac{x^2-3x-10}{x^2+11x-18}$

This next one just says solve, it looks easy but...

$ 3x= \frac {4}{x} - \frac {13}{2} $

- I thought this would be an easy one but I am doing it wrong. It looked like a zero property one where you get everything to equal 0 but I have to get two answers and I am only getting one.

I actually think I said 5 or 6 equations but I dont want to ask too much of someone. If I can understand out how to do these ones on here it would help me better familiarize myself with the type of equations for the test coming. I may have trouble with a few more tomorrow so I may post a couple more here if its not gonna be too much to ask.

Thanks

For the last one, we don't like that fraction terms. so multiply both sides by 2x:

$3x=\frac4x-\frac{13}2\implies 6x^2=8-13x\implies 6x^2+13x-8=0$

This is a quadratic equation. See if you can take it from here!

Does this make sense?

--Chris

**Shrinkwrap** · October 25th 2008, 09:40 PM

sorry, i wasnt at my computer to respond very soon, thanks for the reply...

the last equation I understand now, I knew i was on the right track just wasnt sure where to start. the first two however are a bit of trouble for me still.

the first one after getting the LCD and distributing the (x+3) to the left side, I come out with $\frac{x^2-x+10}{(x+5)(x+3)}$ . This obviously cant be right since I cant find anything to factor the top into and ive retried the problem several times with the same result.

the second one maybe im just not thinking right at the moment but I cant figure out anything to factor out $x^2+11x-18$ . 9 and 2 wont work because it has to be a -2 or -9 with a positive 2 or positive 9 and never adds up to 11.

as you can tell, im not doing very good with factoring this stuff out, i missed the main class that day and it just got worse after each lecture for me. if i could get these two better understood thatd be great, and ill try to be on so I can reply sooner.

thanks again

**Chris L T521** · October 25th 2008, 11:14 PM

Originally Posted by Shrinkwrap

sorry, i wasnt at my computer to respond very soon, thanks for the reply...

the last equation I understand now, I knew i was on the right track just wasnt sure where to start. the first two however are a bit of trouble for me still.

the first one after getting the LCD and distributing the (x+3) to the left side, I come out with $\frac{x^2-x+10}{(x+5)(x+3)}$ . This obviously cant be right since I cant find anything to factor the top into and ive retried the problem several times with the same result.

For the first one, I end up with $\frac{(2x-3)(x+3)}{(x+3)(x+5)}-\frac{x^2-4x-19}{(x+3)(x+5)}$ $=\frac{2x^2+3x-9}{(x+3)(x+5)}-\frac{x^2-4x-19}{(x+3)(x+5)}=\frac{x^2+7x+10}{(x+3)(x+5)}=\frac {(x+2)(x+5)}{(x+3)(x+5)}=\color{red}\boxed{\frac{x +2}{x+3}}$

the second one maybe im just not thinking right at the moment but I cant figure out anything to factor out $x^2+11x-18$ . 9 and 2 wont work because it has to be a -2 or -9 with a positive 2 or positive 9 and never adds up to 11.

I don't see anything either. It may be prime.

However, if the question was $\frac{1 - \displaystyle\frac {3}{x} - \displaystyle\frac {10}{x^2}}{1 + \displaystyle\frac {11}{x} {\color{red}+} \displaystyle\frac {18}{x^2}}$ , then we would end up with $\frac{x^2-3x-10}{x^2+11x+18}=\frac{(x+2)(x-5)}{(x+2)(x+9)}=\color{red}\boxed{\frac{x-5}{x+9}}$

as you can tell, im not doing very good with factoring this stuff out, i missed the main class that day and it just got worse after each lecture for me. if i could get these two better understood thatd be great, and ill try to be on so I can reply sooner.

thanks again

If you have any additional questions, feel free to ask.

--Chris

**Shrinkwrap** · October 26th 2008, 10:48 AM

ahhh thank you lol, i feel really stupid right now. both of those problems I accidently slapped on a negative instead of the positive and no wonder i couldnt figure it out. I got to make sure i dont do that on the exam then. They solve out fine once you fixed the + and on the first one I somehow replaces a negative with a positive a few times. ^_^

thanks again

**Shrinkwrap** · October 26th 2008, 12:17 PM

didnt want to have to bother you with another problem again but I cant figure out this one at all.

$ \frac { \frac {x-1}{x+1}-\frac{x+1}{x-1} } { \frac {x-1}{x+1}+\frac{x+1}{x-1} } $

To simplify, I first did the LCD which was x-1, x+1 and got:
$ \frac {(x-1)^2-(x+1)^2}{(x-1)^2+(x+1)^2} $

Thats about were I am at, and i dunno what to do from there even if what I have sofar is right. Its not making much sense to me because it looks as if I can just cancel the whole equation out the way it looks which would make no sense either. The answer is supposed to be:

$ -\frac {2x}{x^2+1} $

**Chris L T521** · October 26th 2008, 08:04 PM

Originally Posted by Shrinkwrap

didnt want to have to bother you with another problem again but I cant figure out this one at all.

$ \frac { \frac {x-1}{x+1}-\frac{x+1}{x-1} } { \frac {x-1}{x+1}+\frac{x+1}{x-1} } $

To simplify, I first did the LCD which was x-1, x+1 and got:
$ \frac {(x-1)^2-(x+1)^2}{(x-1)^2+(x+1)^2} $

Thats about were I am at, and i dunno what to do from there even if what I have sofar is right. Its not making much sense to me because it looks as if I can just cancel the whole equation out the way it looks which would make no sense either. The answer is supposed to be:

$ -\frac {2x}{x^2+1} $

Foil it out:

$\frac{(x-1)^2-(x+1)^2}{(x-1)^2+(x+1)^2}=\frac{x^2-2x+1-(x^2+2x+1)}{x^2-2x+1+x^2+2x+1}=\frac{-4x}{2x^2+2}$

I'm sure you can take it from here.

--Chris

**Shrinkwrap** · October 26th 2008, 09:19 PM

/facepalm lol thanks, i dunno what i was thinking. I saw ()^2 so I must of gotten confused and thought there was no foiling. thanks... a third time. ^_^

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