## Rational equation: solve 5/y = 3/(7y) + 4/(11y) - 8

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TehNyanCat
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### Rational equation: solve 5/y = 3/(7y) + 4/(11y) - 8

$\frac{5}{y}\, =\, \frac{3}{7y}\,+\,\frac{4}{11y}\,-\,8$
I don't know how to solve this.
I tried multiplying the whole thing by 77y to cancel out the denominators, but I don't think it's working. Am I supposed to do that?
Last edited by TehNyanCat on Sun Jun 19, 2011 4:19 am, edited 1 time in total.

stapel_eliz
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TehNyanCat wrote:$\frac{5}{y}\, =\, \frac{3}{7y}\,+\,\frac{4}{11y}\,-\,8$
I don't know how to solve this.
I tried multiplying the whole thing by 77y to cancel out the denominators, but I don't think it's working. Am I supposed to do that?

Yes, multiplying through is a good first step. What did you get?

TehNyanCat
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### Re:

stapel_eliz wrote:
TehNyanCat wrote:$\frac{5}{y}\, =\, \frac{3}{7y}\,+\,\frac{4}{11y}\,-\,8$
I don't know how to solve this.
I tried multiplying the whole thing by 77y to cancel out the denominators, but I don't think it's working. Am I supposed to do that?

Yes, multiplying through is a good first step. What did you get?

I got $\frac{385}{y}\, =\, \frac{33}{y}\,+\,\frac{28}{y}-616$.

stapel_eliz
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stapel_eliz wrote:Yes, multiplying through is a good first step. What did you get?

TehNyanCat wrote:I got $\frac{385}{y}\, =\, \frac{33}{y}\,+\,\frac{28}{y}-616$.

How did you multiply through by "77y" and still have "y" in the denominator?

TehNyanCat
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### Re:

stapel_eliz wrote:
stapel_eliz wrote:Yes, multiplying through is a good first step. What did you get?

TehNyanCat wrote:I got $\frac{385}{y}\, =\, \frac{33}{y}\,+\,\frac{28}{y}-616$.

How did you multiply through by "77y" and still have "y" in the denominator?

Wait a sec...
I think it's actually 385=33+28-616y. Which, simplified, would be 324=-616y. Then, if the right hand side is divided by -616, the left side would be something like $\frac{324}{-616}$, right?

stapel_eliz
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TehNyanCat wrote:I think it's actually 385=33+28-616y. Which, simplified, would be 324=-616y. Then, if the right hand side is divided by -616, the left side would be something like $\frac{324}{-616}$, right?

The solution to any "solving" problem may be checked by plugging it back into the original exercise. What do you get when you plug in "-324/616" (after simplifying, of course!)?

TehNyanCat
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### Re: Re:

stapel_eliz wrote:
TehNyanCat wrote:I think it's actually 385=33+28-616y. Which, simplified, would be 324=-616y. Then, if the right hand side is divided by -616, the left side would be something like $\frac{324}{-616}$, right?

The solution to any "solving" problem may be checked by plugging it back into the original exercise. What do you get when you plug in "-324/616" (after simplifying, of course!)?

$\frac{-81}{154}$ is the most reduced I can get. So I plug it back in... and oh no...
In LaTeX form, this equation would be waaay too long, so I'm just gonna put in an image:

This just got really frustrating. Any advice on what to do first?

stapel_eliz
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TehNyanCat wrote:$\frac{-81}{154}$ is the most reduced I can get. So I plug it back in... and oh no...

That's the same value I get. Try plugging the whole messy thing into your graphing calculator (where you can use parentheses) or a spreadsheet like Excel.